1
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Deng S, Ódor G. Chimera-like states in neural networks and power systems. CHAOS (WOODBURY, N.Y.) 2024; 34:033135. [PMID: 38526980 DOI: 10.1063/5.0154581] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Accepted: 02/27/2024] [Indexed: 03/27/2024]
Abstract
Partial, frustrated synchronization, and chimera-like states are expected to occur in Kuramoto-like models if the spectral dimension of the underlying graph is low: ds<4. We provide numerical evidence that this really happens in the case of the high-voltage power grid of Europe (ds<2), a large human connectome (KKI113) and in the case of the largest, exactly known brain network corresponding to the fruit-fly (FF) connectome (ds<4), even though their graph dimensions are much higher, i.e., dgEU≃2.6(1) and dgFF≃5.4(1), dgKKI113≃3.4(1). We provide local synchronization results of the first- and second-order (Shinomoto) Kuramoto models by numerical solutions on the FF and the European power-grid graphs, respectively, and show the emergence of chimera-like patterns on the graph community level as well as by the local order parameters.
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Affiliation(s)
- Shengfeng Deng
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Géza Ódor
- Institute of Technical Physics and Materials Science, HUN-REN Centre for Energy Research, P.O. Box 49, Budapest H-1525, Hungary
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2
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Papo D, Buldú JM. Does the brain behave like a (complex) network? I. Dynamics. Phys Life Rev 2024; 48:47-98. [PMID: 38145591 DOI: 10.1016/j.plrev.2023.12.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 12/10/2023] [Indexed: 12/27/2023]
Abstract
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.
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Affiliation(s)
- D Papo
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, Ferrara, Italy; Center for Translational Neurophysiology, Fondazione Istituto Italiano di Tecnologia, Ferrara, Italy.
| | - J M Buldú
- Complex Systems Group & G.I.S.C., Universidad Rey Juan Carlos, Madrid, Spain
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3
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Mishra A, Saha S, Dana SK. Chimeras in globally coupled oscillators: A review. CHAOS (WOODBURY, N.Y.) 2023; 33:092101. [PMID: 37703474 DOI: 10.1063/5.0143872] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2023] [Accepted: 08/21/2023] [Indexed: 09/15/2023]
Abstract
The surprising phenomenon of chimera in an ensemble of identical oscillators is no more strange behavior of network dynamics and reality. By this time, this symmetry breaking self-organized collective dynamics has been established in many networks, a ring of non-locally coupled oscillators, globally coupled networks, a three-dimensional network, and multi-layer networks. A variety of coupling and dynamical models in addition to the phase oscillators has been used for a successful observation of chimera patterns. Experimental verification has also been done using metronomes, pendula, chemical, and opto-electronic systems. The phenomenon has also been shown to appear in small networks, and hence, it is not size-dependent. We present here a brief review of the origin of chimera patterns restricting our discussions to networks of globally coupled identical oscillators only. The history of chimeras in globally coupled oscillators is older than what has been reported in nonlocally coupled phase oscillators much later. We elaborate the story of the origin of chimeras in globally coupled oscillators in a chronological order, within our limitations, and with brief descriptions of the significant contributions, including our personal experiences. We first introduce chimeras in non-locally coupled and other network configurations, in general, and then discuss about globally coupled networks in more detail.
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Affiliation(s)
- Arindam Mishra
- Department of Physics, National University of Singapore, Singapore 117551
| | - Suman Saha
- Cognitive Brain Dynamics Laboratory, National Brain Research Centre, Gurugram 122051, India
| | - Syamal K Dana
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
- Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland
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4
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Zhu J, Yamakou ME. Self-induced-stochastic-resonance breathing chimeras. Phys Rev E 2023; 108:L022204. [PMID: 37723731 DOI: 10.1103/physreve.108.l022204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Accepted: 07/22/2023] [Indexed: 09/20/2023]
Abstract
The study by Semenova et al. [Phys. Rev. Lett. 117, 014102 (2016)0031-900710.1103/PhysRevLett.117.014102] discovered a type of chimera state known as coherence-resonance chimera (CRC), which combines the effects of coherence resonance (CR) and the spatial property of classical chimeras. In this Letter, we present yet another form of chimera, which we refer to as self-induced-stochastic-resonance breathing chimera (SISR-BC), which differs fundamentally from the CRC in that it combines the mechanism and effects of self-induced stochastic resonance (SISR, previously shown by DeVille et al. [Phys. Rev. E 72, 031105 (2005)1539-375510.1103/PhysRevE.72.031105] to be intrinsically different from CR), the symmetry breaking in the rotational coupling between the slow and fast subsystems of the coupled oscillators, and the property of breathing chimera-a form of chimera state characterized by nonstationary periodic dynamics of coherent-incoherent patterns with a periodically oscillating global order parameter. Unlike other types of chimeras, including CRC, SISR-BC demonstrates remarkable resilience to a relatively wide range of stochastic perturbations and persists even when the purely excitable system is significantly distant from the Hopf bifurcation threshold-thanks to the mechanism of SISR-and globally attracts random distributions of initial conditions. Considering its potential impact on information processing in neuronal networks, SISR-BC could have special significance and applications.
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Affiliation(s)
- Jinjie Zhu
- State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
| | - Marius E Yamakou
- Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
- Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22, 04103 Leipzig, Germany
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5
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Andrzejak RG, Espinoso A. Chimera states in multiplex networks: Chameleon-like across-layer synchronization. CHAOS (WOODBURY, N.Y.) 2023; 33:2890080. [PMID: 37163994 DOI: 10.1063/5.0146550] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 04/19/2023] [Indexed: 05/12/2023]
Abstract
Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators' mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups' position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.
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Affiliation(s)
- Ralph G Andrzejak
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
| | - Anaïs Espinoso
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
- Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology, Carrer Baldiri Reixac 10-12, 08028 Barcelona, Catalonia, Spain
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6
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Kundu S, Ghosh D. Higher-order interactions promote chimera states. Phys Rev E 2022; 105:L042202. [PMID: 35590617 DOI: 10.1103/physreve.105.l042202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2022] [Accepted: 03/31/2022] [Indexed: 06/15/2023]
Abstract
Since the discovery of chimera states, the presence of a nonzero phase lag parameter turns out to be an essential attribute for the emergence of chimeras in a nonlocally coupled identical Kuramoto phase oscillators' network with pairwise interactions. In this Letter, we report the emergence of chimeras without phase lag in a nonlocally coupled identical Kuramoto network owing to the introduction of nonpairwise interactions. The influence of added nonlinearity in the coupled system dynamics in the form of simplicial complexes mitigates the requisite of a nonzero phase lag parameter for the emergence of chimera states. Chimera states stimulated by the reciprocity of the pairwise and nonpairwise interaction strengths and their multistable nature are characterized with appropriate measures and are demonstrated in the parameter spaces.
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Affiliation(s)
- Srilena Kundu
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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7
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Majhi S, Rakshit S, Ghosh D. Oscillation suppression and chimera states in time-varying networks. CHAOS (WOODBURY, N.Y.) 2022; 32:042101. [PMID: 35489845 DOI: 10.1063/5.0087291] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2022] [Accepted: 03/11/2022] [Indexed: 06/14/2023]
Abstract
Complex network theory has offered a powerful platform for the study of several natural dynamic scenarios, based on the synergy between the interaction topology and the dynamics of its constituents. With research in network theory being developed so fast, it has become extremely necessary to move from simple network topologies to more sophisticated and realistic descriptions of the connectivity patterns. In this context, there is a significant amount of recent works that have emerged with enormous evidence establishing the time-varying nature of the connections among the constituents in a large number of physical, biological, and social systems. The recent review article by Ghosh et al. [Phys. Rep. 949, 1-63 (2022)] demonstrates the significance of the analysis of collective dynamics arising in temporal networks. Specifically, the authors put forward a detailed excerpt of results on the origin and stability of synchronization in time-varying networked systems. However, among the complex collective dynamical behaviors, the study of the phenomenon of oscillation suppression and that of other diverse aspects of synchronization are also considered to be central to our perception of the dynamical processes over networks. Through this review, we discuss the principal findings from the research studies dedicated to the exploration of the two collective states, namely, oscillation suppression and chimera on top of time-varying networks of both static and mobile nodes. We delineate how temporality in interactions can suppress oscillation and induce chimeric patterns in networked dynamical systems, from effective analytical approaches to computational aspects, which is described while addressing these two phenomena. We further sketch promising directions for future research on these emerging collective behaviors in time-varying networks.
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Affiliation(s)
- Soumen Majhi
- Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | - Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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8
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Chimera states and cluster solutions in Hindmarsh-Rose neural networks with state resetting process. Cogn Neurodyn 2022; 16:215-228. [PMID: 35126779 PMCID: PMC8807783 DOI: 10.1007/s11571-021-09691-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2020] [Revised: 05/24/2021] [Accepted: 06/11/2021] [Indexed: 02/03/2023] Open
Abstract
The neuronal state resetting model is a hybrid system, which combines neuronal system with state resetting process. As the membrane potential reaches a certain threshold, the membrane potential and recovery current are reset. Through the resetting process, the neuronal system can produce abundant new firing patterns. By integrating with the state resetting process, the neuronal system can generate irregular limit cycles (limit cycles with impulsive breakpoints), resulting in repetitive spiking or bursting with firing peaks which can not exceed a presetting threshold. Although some studies have discussed the state resetting process in neurons, it has not been addressed in neural networks so far. In this paper, we consider chimera states and cluster solutions in Hindmarsh-Rose neural networks with state resetting process. The network structures are based on regular ring structures and the connections among neurons are assumed to be bidirectional. Chimera and cluster states are two types of phenomena related to synchronization. For neural networks, the chimera state is a self-organization phenomenon in which some neuronal nodes are synchronous while the others are asynchronous. Cluster synchronization divides the system into several subgroups based on their synchronization characteristics, with neuronal nodes in each subgroup being synchronous. By improving previous chimera measures, we detect the spike inspire time instead of the state variable and calculate the time between two adjacent spikes. We then discuss the incoherence, chimera state, and coherence of the constructed neural networks using phase diagrams, time series diagrams, and probability density histograms. Besides, we further contrast the cluster solutions of the system under local and global coupling, respectively. The subordinate state resetting process enriches the firing mode of the proposed Hindmarsh-Rose neural networks.
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Asllani M, Siebert BA, Arenas A, Gleeson JP. Symmetry-breaking mechanism for the formation of cluster chimera patterns. CHAOS (WOODBURY, N.Y.) 2022; 32:013107. [PMID: 35105109 DOI: 10.1063/5.0060466] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2021] [Accepted: 12/06/2021] [Indexed: 06/14/2023]
Abstract
The emergence of order in collective dynamics is a fascinating phenomenon that characterizes many natural systems consisting of coupled entities. Synchronization is such an example where individuals, usually represented by either linear or nonlinear oscillators, can spontaneously act coherently with each other when the interactions' configuration fulfills certain conditions. However, synchronization is not always perfect, and the coexistence of coherent and incoherent oscillators, broadly known in the literature as chimera states, is also possible. Although several attempts have been made to explain how chimera states are created, their emergence, stability, and robustness remain a long-debated question. We propose an approach that aims to establish a robust mechanism through which cluster synchronization and chimera patterns originate. We first introduce a stability-breaking method where clusters of synchronized oscillators can emerge. At variance with the standard approach where synchronization arises as a collective behavior of coupled oscillators, in our model, the system initially sets on a homogeneous fixed-point regime, and, only due to a global instability principle, collective oscillations emerge. Following a combination of the network modularity and the model's parameters, one or more clusters of oscillators become incoherent within yielding a particular class of patterns that we here name cluster chimera states.
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Affiliation(s)
- Malbor Asllani
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland
| | - Bram A Siebert
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
| | - Alex Arenas
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Catalonia, Spain
| | - James P Gleeson
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
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10
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Clusella P, Pietras B, Montbrió E. Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling. CHAOS (WOODBURY, N.Y.) 2022; 32:013105. [PMID: 35105122 DOI: 10.1063/5.0075285] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Accepted: 12/13/2021] [Indexed: 06/14/2023]
Abstract
We derive the Kuramoto model (KM) corresponding to a population of weakly coupled, nearly identical quadratic integrate-and-fire (QIF) neurons with both electrical and chemical coupling. The ratio of chemical to electrical coupling determines the phase lag of the characteristic sine coupling function of the KM and critically determines the synchronization properties of the network. We apply our results to uncover the presence of chimera states in two coupled populations of identical QIF neurons. We find that the presence of both electrical and chemical coupling is a necessary condition for chimera states to exist. Finally, we numerically demonstrate that chimera states gradually disappear as coupling strengths cease to be weak.
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Affiliation(s)
- Pau Clusella
- Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park, 08003 Barcelona, Spain
| | - Bastian Pietras
- Institute of Mathematics, Technical University Berlin, 10623 Berlin, Germany
| | - Ernest Montbrió
- Neuronal Dynamics Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain
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11
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Goodfellow M, Andrzejak RG, Masoller C, Lehnertz K. What Models and Tools can Contribute to a Better Understanding of Brain Activity? FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:907995. [PMID: 36926061 PMCID: PMC10013030 DOI: 10.3389/fnetp.2022.907995] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 06/06/2022] [Indexed: 12/18/2022]
Abstract
Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.
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Affiliation(s)
- Marc Goodfellow
- Living Systems Institute, University of Exeter, Exeter, United Kingdom
| | - Ralph G Andrzejak
- Department of Information and Communication Technologies, University Pompeu Fabra, Barcelona, Spain
| | - Cristina Masoller
- Department of Physics, Universitat Politecnica de Catalunya, Barcelona, Spain
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany.,Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany.,Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
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12
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The diversity and multiplexity of edge communities within and between brain systems. Cell Rep 2021; 37:110032. [PMID: 34788617 DOI: 10.1016/j.celrep.2021.110032] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2021] [Revised: 09/08/2021] [Accepted: 10/28/2021] [Indexed: 11/24/2022] Open
Abstract
The human brain is composed of functionally specialized systems that support cognition. Recently, we proposed an edge-centric model for detecting overlapping communities. It remains unclear how these communities and brain systems are related. Here, we address this question using data from the Midnight Scan Club and show that all brain systems are linked via at least two edge communities. We then examine the diversity of edge communities within each system, finding that heteromodal systems are more diverse than sensory systems. Next, we cluster the entire cortex to reveal it according to the regions' edge-community profiles. We find that regions in heteromodal systems are more likely to form their own clusters. Finally, we show that edge communities are personalized. Our work reveals the pervasive overlap of edge communities across the cortex and their relationship with brain systems. Our work provides pathways for future research using edge-centric brain networks.
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Jaros P, Levchenko R, Kapitaniak T, Maistrenko Y. Chimera states for directed networks. CHAOS (WOODBURY, N.Y.) 2021; 31:103111. [PMID: 34717326 DOI: 10.1063/5.0059765] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 09/28/2021] [Indexed: 06/13/2023]
Abstract
We demonstrate that chimera behavior can be observed in ensembles of phase oscillators with unidirectional coupling. For a small network consisting of only three identical oscillators (cyclic triple), tiny chimera islands arise in the parameter space. They are surrounded by developed chaotic switching behavior caused by a collision of rotating waves propagating in opposite directions. For larger networks, as we show for a hundred oscillators (cyclic century), the islands merge into a single chimera continent, which incorporates the world of chimeras of different configurations. The phenomenon inherits from networks with intermediate ranges of the unidirectional coupling and it diminishes as the coupling range decreases.
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Affiliation(s)
- Patrycja Jaros
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | | | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Yuri Maistrenko
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
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14
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Tsigkri-DeSmedt ND, Sarlis NV, Provata A. Shooting solitaries due to small-world connectivity in leaky integrate-and-fire networks. CHAOS (WOODBURY, N.Y.) 2021; 31:083129. [PMID: 34470234 DOI: 10.1063/5.0055163] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Accepted: 07/30/2021] [Indexed: 06/13/2023]
Abstract
We study the synchronization properties in a network of leaky integrate-and-fire oscillators with nonlocal connectivity under probabilistic small-world rewiring. We demonstrate that the random links lead to the emergence of chimera-like states where the coherent regions are interrupted by scattered, short-lived solitaries; these are termed "shooting solitaries." Moreover, we provide evidence that random links enhance the appearance of chimera-like states for values of the parameter space that otherwise support synchronization. This last effect is counter-intuitive because by adding random links to the synchronous state, the system locally organizes into coherent and incoherent domains.
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Affiliation(s)
- N D Tsigkri-DeSmedt
- Section of Condensed Matter Physics, Physics Department, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, 157 84 Athens, Greece
| | - N V Sarlis
- Section of Condensed Matter Physics, Physics Department, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, 157 84 Athens, Greece
| | - A Provata
- Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos", Agia Paraskevi, 153 10 Athens, Greece
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15
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Bera BK, Kundu S, Muruganandam P, Ghosh D, Lakshmanan M. Spiral wave chimera-like transient dynamics in three-dimensional grid of diffusive ecological systems. CHAOS (WOODBURY, N.Y.) 2021; 31:083125. [PMID: 34470253 DOI: 10.1063/5.0062566] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Accepted: 08/04/2021] [Indexed: 06/13/2023]
Abstract
In the present article, we demonstrate the emergence and existence of the spiral wave chimera-like transient pattern in coupled ecological systems, composed of prey-predator patches, where the patches are connected in a three-dimensional medium through local diffusion. We explore the transition scenarios among several collective dynamical behaviors together with transient spiral wave chimera-like states and investigate the long time behavior of these states. The transition from the transient spiral chimera-like pattern to the long time synchronized or desynchronized pattern appears through the deformation of the incoherent region of the spiral core. We discuss the transient dynamics under the influence of the species diffusion at different time instants. By calculating the instantaneous strength of incoherence of the populations, we estimate the duration of the transient dynamics characterized by the persistence of the chimera-like spatial coexistence of coherent and incoherent patterns over the spatial domain. We generalize our observations on the transient dynamics in a three-dimensional grid of diffusive ecological systems by considering two different prey-predator systems.
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Affiliation(s)
- Bidesh K Bera
- Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
| | - Srilena Kundu
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | | | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - M Lakshmanan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620024, India
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16
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Brezetsky S, Jaros P, Levchenko R, Kapitaniak T, Maistrenko Y. Chimera complexity. Phys Rev E 2021; 103:L050204. [PMID: 34134258 DOI: 10.1103/physreve.103.l050204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2020] [Accepted: 04/23/2021] [Indexed: 06/12/2023]
Abstract
We show an amazing complexity of the chimeras in small networks of coupled phase oscillators with inertia. The network behavior is characterized by heteroclinic switching between multiple saddle chimera states and riddling basins of attractions, causing an extreme sensitivity to initial conditions and parameters. Additional uncertainty is induced by the presumable coexistence of stable phase-locked states or other stable chimeras as the switching trajectories can eventually tend to them. The system dynamics becomes hardly predictable, while its complexity represents a challenge in the network sciences.
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Affiliation(s)
- Serhiy Brezetsky
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Patrycja Jaros
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Roman Levchenko
- Faculty of Radiophysics, Electronics and Computer Systems, Taras Shevchenko National University of Kyiv, Volodymyrska St. 60, 01030 Kyiv, Ukraine
- Forschungszentrum Jülich, 52428 Jülich, Germany
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Yuri Maistrenko
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
- Forschungszentrum Jülich, 52428 Jülich, Germany
- Institute of Mathematics and Centre for Medical and Biotechnical Research, NAS of Ukraine, Tereshchenkivska St. 3, 01030 Kyiv, Ukraine
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Shepelev IA, Muni SS, Vadivasova TE. Synchronization of wave structures in a heterogeneous multiplex network of 2D lattices with attractive and repulsive intra-layer coupling. CHAOS (WOODBURY, N.Y.) 2021; 31:021104. [PMID: 33653058 DOI: 10.1063/5.0044327] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2021] [Accepted: 02/04/2021] [Indexed: 06/12/2023]
Abstract
We explore numerically the synchronization effects in a heterogeneous two-layer network of two-dimensional (2D) lattices of van der Pol oscillators. The inter-layer coupling of the multiplex network has an attractive character. One layer of 2D lattices is characterized by attractive coupling of oscillators and demonstrates a spiral wave regime for both local and nonlocal interactions. The oscillators in the second layer are coupled through active elements and the interaction between them has repulsive character. We show that the lattice with the repulsive type of coupling demonstrates complex spatiotemporal cluster structures, which can be called labyrinth-like structures. We show for the first time that this multiplex network with fundamentally various types of intra-layer coupling demonstrates mutual synchronization and a competition between two types of structures. Our numerical study indicates that the synchronization threshold and the type of spatiotemporal patterns in both layers strongly depend on the ratio of the intra-layer coupling strength of the two lattices. We also analyze the impact of intra-layer coupling ranges on the synchronization effects.
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Affiliation(s)
- I A Shepelev
- Department of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - S S Muni
- School of Fundamental Sciences, Massey University, Palmerston North 4442, New Zealand
| | - T E Vadivasova
- Department of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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18
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Maertens T, Schöll E, Ruiz J, Hövel P. Multilayer network analysis of C. elegans: Looking into the locomotory circuitry. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.11.015] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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19
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Forro C, Caron D, Angotzi GN, Gallo V, Berdondini L, Santoro F, Palazzolo G, Panuccio G. Electrophysiology Read-Out Tools for Brain-on-Chip Biotechnology. MICROMACHINES 2021; 12:124. [PMID: 33498905 PMCID: PMC7912435 DOI: 10.3390/mi12020124] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Revised: 01/18/2021] [Accepted: 01/19/2021] [Indexed: 02/07/2023]
Abstract
Brain-on-Chip (BoC) biotechnology is emerging as a promising tool for biomedical and pharmaceutical research applied to the neurosciences. At the convergence between lab-on-chip and cell biology, BoC couples in vitro three-dimensional brain-like systems to an engineered microfluidics platform designed to provide an in vivo-like extrinsic microenvironment with the aim of replicating tissue- or organ-level physiological functions. BoC therefore offers the advantage of an in vitro reproduction of brain structures that is more faithful to the native correlate than what is obtained with conventional cell culture techniques. As brain function ultimately results in the generation of electrical signals, electrophysiology techniques are paramount for studying brain activity in health and disease. However, as BoC is still in its infancy, the availability of combined BoC-electrophysiology platforms is still limited. Here, we summarize the available biological substrates for BoC, starting with a historical perspective. We then describe the available tools enabling BoC electrophysiology studies, detailing their fabrication process and technical features, along with their advantages and limitations. We discuss the current and future applications of BoC electrophysiology, also expanding to complementary approaches. We conclude with an evaluation of the potential translational applications and prospective technology developments.
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Affiliation(s)
- Csaba Forro
- Tissue Electronics, Fondazione Istituto Italiano di Tecnologia, Largo Barsanti e Matteucci, 53-80125 Naples, Italy; (C.F.); (F.S.)
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA
| | - Davide Caron
- Enhanced Regenerative Medicine, Fondazione Istituto Italiano di Tecnologia, Via Morego, 30-16163 Genova, Italy; (D.C.); (V.G.)
| | - Gian Nicola Angotzi
- Microtechnology for Neuroelectronics, Fondazione Istituto Italiano di Tecnologia, Via Morego, 30-16163 Genova, Italy; (G.N.A.); (L.B.)
| | - Vincenzo Gallo
- Enhanced Regenerative Medicine, Fondazione Istituto Italiano di Tecnologia, Via Morego, 30-16163 Genova, Italy; (D.C.); (V.G.)
| | - Luca Berdondini
- Microtechnology for Neuroelectronics, Fondazione Istituto Italiano di Tecnologia, Via Morego, 30-16163 Genova, Italy; (G.N.A.); (L.B.)
| | - Francesca Santoro
- Tissue Electronics, Fondazione Istituto Italiano di Tecnologia, Largo Barsanti e Matteucci, 53-80125 Naples, Italy; (C.F.); (F.S.)
| | - Gemma Palazzolo
- Enhanced Regenerative Medicine, Fondazione Istituto Italiano di Tecnologia, Via Morego, 30-16163 Genova, Italy; (D.C.); (V.G.)
| | - Gabriella Panuccio
- Enhanced Regenerative Medicine, Fondazione Istituto Italiano di Tecnologia, Via Morego, 30-16163 Genova, Italy; (D.C.); (V.G.)
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20
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Dudkowski D, Czołczyński K, Kapitaniak T. Multi-headed loop chimera states in coupled oscillators. CHAOS (WOODBURY, N.Y.) 2021; 31:013135. [PMID: 33754776 DOI: 10.1063/5.0033519] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Accepted: 01/05/2021] [Indexed: 06/12/2023]
Abstract
In this paper, we introduce a novel type of chimera state, characterized by the geometrical distortion of the coherent ring topology of coupled oscillators. The multi-headed loop chimeras are examined for a simple network of locally coupled pendulum clocks, suspended on the vertical platform. We determine the regions of the occurrence of the observed patterns, their structure, and possible co-existence. The representative examples of behaviors are shown, exhibiting the variety of configurations that can be observed. The statistical analysis of the solutions indicates the geometrical regions of the system with the highest probability of the chimeras' occurrence. We investigate the mechanism of the creation of the observed states, showing that the manipulation of the initial positions of chosen pendula may induce the desired patterns. Apart from the study of the isolated network, we also discuss the scenario of the movable platform, showing a possible influence of the global coupling structure on the stability of the observed states. The stability of loop chimeras is examined for varying both the amplitude and the frequency of the oscillations of the platform. We indicate the excitation parameters for which the solutions can survive as well as be destroyed. The bifurcation analysis included in the paper allows us to discuss the transitions between possible behaviors. The appearance of multi-headed loop chimeras is generalized into large networks of oscillators, showing the universal character of the observed patterns. One should expect to observe similar results also in other types of coupled oscillators, especially the mechanical ones.
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Affiliation(s)
- Dawid Dudkowski
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Krzysztof Czołczyński
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
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21
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Huo S, Tian C, Zheng M, Guan S, Zhou C, Liu Z. Spatial multi-scaled chimera states of cerebral cortex network and its inherent structure-dynamics relationship in human brain. Natl Sci Rev 2021; 8:nwaa125. [PMID: 34691552 PMCID: PMC8288421 DOI: 10.1093/nsr/nwaa125] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2019] [Revised: 04/01/2020] [Accepted: 05/21/2020] [Indexed: 11/20/2022] Open
Abstract
Human cerebral cortex displays various dynamics patterns under different states, however the mechanism how such diverse patterns can be supported by the underlying brain network is still not well understood. Human brain has a unique network structure with different regions of interesting to perform cognitive tasks. Using coupled neural mass oscillators on human cortical network and paying attention to both global and local regions, we observe a new feature of chimera states with multiple spatial scales and a positive correlation between the synchronization preference of local region and the degree of symmetry of the connectivity of the region in the network. Further, we use the concept of effective symmetry in the network to build structural and dynamical hierarchical trees and find close matching between them. These results help to explain the multiple brain rhythms observed in experiments and suggest a generic principle for complex brain network as a structure substrate to support diverse functional patterns.
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Affiliation(s)
- Siyu Huo
- State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China
| | - Changhai Tian
- State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China
- School of Data Science, Tongren University, Tongren 554300, China
| | - Muhua Zheng
- State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China
| | - Shuguang Guan
- State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China
| | - Changsong Zhou
- Department of Physics, Centre for Nonlinear Studies and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Institute of Computational and Theoretical Studies, Hong Kong Baptist University, China
- Department of Physics, Zhejiang University, Hangzhou 310058, China
| | - Zonghua Liu
- State Key Laboratory of Precision Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China
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22
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Controlling the Chimera Form in the Leaky Integrate-and-Fire Model. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2021; 1338:247-258. [DOI: 10.1007/978-3-030-78775-2_30] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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23
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Protachevicz PR, Iarosz KC, Caldas IL, Antonopoulos CG, Batista AM, Kurths J. Influence of Autapses on Synchronization in Neural Networks With Chemical Synapses. Front Syst Neurosci 2020; 14:604563. [PMID: 33328913 PMCID: PMC7734146 DOI: 10.3389/fnsys.2020.604563] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Accepted: 11/05/2020] [Indexed: 11/29/2022] Open
Abstract
A great deal of research has been devoted on the investigation of neural dynamics in various network topologies. However, only a few studies have focused on the influence of autapses, synapses from a neuron onto itself via closed loops, on neural synchronization. Here, we build a random network with adaptive exponential integrate-and-fire neurons coupled with chemical synapses, equipped with autapses, to study the effect of the latter on synchronous behavior. We consider time delay in the conductance of the pre-synaptic neuron for excitatory and inhibitory connections. Interestingly, in neural networks consisting of both excitatory and inhibitory neurons, we uncover that synchronous behavior depends on their synapse type. Our results provide evidence on the synchronous and desynchronous activities that emerge in random neural networks with chemical, inhibitory and excitatory synapses where neurons are equipped with autapses.
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Affiliation(s)
| | - Kelly C Iarosz
- Faculdade de Telêmaco Borba, FATEB, Telêmaco Borba, Brazil.,Graduate Program in Chemical Engineering, Federal University of Technology Paraná, Ponta Grossa, Brazil
| | - Iberê L Caldas
- Institute of Physics, University of São Paulo, São Paulo, Brazil
| | - Chris G Antonopoulos
- Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom
| | - Antonio M Batista
- Institute of Physics, University of São Paulo, São Paulo, Brazil.,Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa, Brazil
| | - Jurgen Kurths
- Department Complexity Science, Potsdam Institute for Climate Impact Research, Potsdam, Germany.,Department of Physics, Humboldt University, Berlin, Germany.,Centre for Analysis of Complex Systems, Sechenov First Moscow State Medical University, Moscow, Russia
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24
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Ruzzene G, Omelchenko I, Sawicki J, Zakharova A, Schöll E, Andrzejak RG. Remote pacemaker control of chimera states in multilayer networks of neurons. Phys Rev E 2020; 102:052216. [PMID: 33327161 DOI: 10.1103/physreve.102.052216] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2020] [Accepted: 10/30/2020] [Indexed: 06/12/2023]
Abstract
Networks of coupled nonlinear oscillators allow for the formation of nontrivial partially synchronized spatiotemporal patterns, such as chimera states, in which there are coexisting coherent (synchronized) and incoherent (desynchronized) domains. These complementary domains form spontaneously, and it is impossible to predict where the synchronized group will be positioned within the network. Therefore, possible ways to control the spatial position of the coherent and incoherent groups forming the chimera states are of high current interest. In this work we investigate how to control chimera patterns in multiplex networks of FitzHugh-Nagumo neurons, and in particular we want to prove that it is possible to remotely control chimera states exploiting the multiplex structure. We introduce a pacemaker oscillator within the network: this is an oscillator that does not receive input from the rest of the network but is sending out information to its neighbors. The pacemakers can be positioned in one or both layers. Their presence breaks the spatial symmetry of the layer in which they are introduced and allows us to control the position of the incoherent domain. We demonstrate how the remote control is possible for both uni- and bidirectional coupling between the layers. Furthermore we show which are the limitations of our control mechanisms when it is generalized from single-layer to multilayer networks.
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Affiliation(s)
- Giulia Ruzzene
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
| | - Iryna Omelchenko
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Jakub Sawicki
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Ralph G Andrzejak
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
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25
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Basios V, Antonopoulos CG, Latifi A. Labyrinth chaos: Revisiting the elegant, chaotic, and hyperchaotic walks. CHAOS (WOODBURY, N.Y.) 2020; 30:113129. [PMID: 33261363 DOI: 10.1063/5.0022253] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2020] [Accepted: 10/26/2020] [Indexed: 06/12/2023]
Abstract
Labyrinth chaos was discovered by Otto Rössler and René Thomas in their endeavor to identify the necessary mathematical conditions for the appearance of chaotic and hyperchaotic motion in continuous flows. Here, we celebrate their discovery by considering a single labyrinth walk system and an array of coupled labyrinth chaos systems that exhibit complex, chaotic behavior, reminiscent of chimera-like states, a peculiar synchronization phenomenon. We discuss the properties of the single labyrinth walk system and review the ability of coupled labyrinth chaos systems to exhibit chimera-like states due to the unique properties of their space-filling, chaotic trajectories, which amounts to elegant, hyperchaotic walks. Finally, we discuss further implications in relation to the labyrinth walk system by showing that even though it is volume-preserving, it is not force-conservative.
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Affiliation(s)
- Vasileios Basios
- Service de Physique des Systèmes Complexes et Mécanique Statistique and Interdisciplinary Center for Nonlinear Phenomena and Complex Systems (CeNoLi), Université Libre de Bruxelles, BE-1050 Ixelles, Belgium
| | - Chris G Antonopoulos
- Department of Mathematical Sciences, University of Essex, Colchester Campus, Colchester CO4 3SQ, United Kingdom
| | - Anouchah Latifi
- Department of Physics, Faculty of Sciences, Qom University of Technology, 1519-37195 Qom, Iran
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26
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Frolov N, Maksimenko V, Majhi S, Rakshit S, Ghosh D, Hramov A. Chimera-like behavior in a heterogeneous Kuramoto model: The interplay between attractive and repulsive coupling. CHAOS (WOODBURY, N.Y.) 2020; 30:081102. [PMID: 32872824 DOI: 10.1063/5.0019200] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Accepted: 07/22/2020] [Indexed: 06/11/2023]
Abstract
Interaction within an ensemble of coupled nonlinear oscillators induces a variety of collective behaviors. One of the most fascinating is a chimera state that manifests the coexistence of spatially distinct populations of coherent and incoherent elements. Understanding of the emergent chimera behavior in controlled experiments or real systems requires a focus on the consideration of heterogeneous network models. In this study, we explore the transitions in a heterogeneous Kuramoto model under the monotonical increase of the coupling strength and specifically find that this system exhibits a frequency-modulated chimera-like pattern during the explosive transition to synchronization. We demonstrate that this specific dynamical regime originates from the interplay between (the evolved) attractively and repulsively coupled subpopulations. We also show that the above-mentioned chimera-like state is induced under weakly non-local, small-world, and sparse scale-free coupling and suppressed in globally coupled, strongly rewired, and dense scale-free networks due to the emergence of the large-scale connections.
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Affiliation(s)
- Nikita Frolov
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
| | - Vladimir Maksimenko
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
| | - Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Alexander Hramov
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, The Republic of Tatarstan, Russia
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27
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Wang Z, Liu Z. A Brief Review of Chimera State in Empirical Brain Networks. Front Physiol 2020; 11:724. [PMID: 32714208 PMCID: PMC7344215 DOI: 10.3389/fphys.2020.00724] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Accepted: 06/02/2020] [Indexed: 11/24/2022] Open
Abstract
Understanding the human brain and its functions has always been an interesting and challenging problem. Recently, a significant progress on this problem has been achieved on the aspect of chimera state where a coexistence of synchronized and unsynchronized states can be sustained in identical oscillators. This counterintuitive phenomenon is closely related to the unihemispheric sleep in some marine mammals and birds and has recently gotten a hot attention in neural systems, except the previous studies in non-neural systems such as phase oscillators. This review will briefly summarize the main results of chimera state in neuronal systems and pay special attention to the network of cerebral cortex, aiming to accelerate the study of chimera state in brain networks. Some outlooks are also discussed.
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Affiliation(s)
| | - Zonghua Liu
- School of Physics and Electronic Science, East China Normal University, Shanghai, China
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28
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Chimera states in hybrid coupled neuron populations. Neural Netw 2020; 126:108-117. [DOI: 10.1016/j.neunet.2020.03.002] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Revised: 02/03/2020] [Accepted: 03/02/2020] [Indexed: 01/01/2023]
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29
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Ganaie MA, Ghosh S, Mendola N, Tanveer M, Jalan S. Identification of chimera using machine learning. CHAOS (WOODBURY, N.Y.) 2020; 30:063128. [PMID: 32611090 DOI: 10.1063/1.5143285] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2019] [Accepted: 05/07/2020] [Indexed: 06/11/2023]
Abstract
Chimera state refers to the coexistence of coherent and non-coherent phases in identically coupled dynamical units found in various complex dynamical systems. Identification of chimera, on one hand, is essential due to its applicability in various areas including neuroscience and, on the other hand, is challenging due to its widely varied appearance in different systems and the peculiar nature of its profile. Therefore, a simple yet universal method for its identification remains an open problem. Here, we present a very distinctive approach using machine learning techniques to characterize different dynamical phases and identify the chimera state from given spatial profiles generated using various different models. The experimental results show that the performance of the classification algorithms varies for different dynamical models. The machine learning algorithms, namely, random forest, oblique random forest based on Tikhonov, axis-parallel split, and null space regularization achieved more than 96% accuracy for the Kuramoto model. For the logistic maps, random forest and Tikhonov regularization based oblique random forest showed more than 90% accuracy, and for the Hénon map model, random forest, null space, and axis-parallel split regularization based oblique random forest achieved more than 80% accuracy. The oblique random forest with null space regularization achieved consistent performance (more than 83% accuracy) across different dynamical models while the auto-encoder based random vector functional link neural network showed relatively lower performance. This work provides a direction for employing machine learning techniques to identify dynamical patterns arising in coupled non-linear units on large-scale and for characterizing complex spatiotemporal patterns in real-world systems for various applications.
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Affiliation(s)
- M A Ganaie
- Discipline of Mathematics, Indian Institute of Technology Indore, Khandwa Road, Simrol, 453552 Indore, India
| | - Saptarshi Ghosh
- Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, 453552 Indore, India
| | - Naveen Mendola
- Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, 453552 Indore, India
| | - M Tanveer
- Discipline of Mathematics, Indian Institute of Technology Indore, Khandwa Road, Simrol, 453552 Indore, India
| | - Sarika Jalan
- Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, 453552 Indore, India
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30
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Brister BN, Belykh VN, Belykh IV. When three is a crowd: Chaos from clusters of Kuramoto oscillators with inertia. Phys Rev E 2020; 101:062206. [PMID: 32688588 DOI: 10.1103/physreve.101.062206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2020] [Accepted: 06/01/2020] [Indexed: 06/11/2023]
Abstract
Modeling cooperative dynamics using networks of phase oscillators is common practice for a wide spectrum of biological and technological networks, ranging from neuronal populations to power grids. In this paper we study the emergence of stable clusters of synchrony with complex intercluster dynamics in a three-population network of identical Kuramoto oscillators with inertia. The populations have different sizes and can split into clusters where the oscillators synchronize within a cluster, but notably, there is a phase shift between the dynamics of the clusters. We extend our previous results on the bistability of synchronized clusters in a two-population network [I. V. Belykh et al., Chaos 26, 094822 (2016)CHAOEH1054-150010.1063/1.4961435] and demonstrate that the addition of a third population can induce chaotic intercluster dynamics. This effect can be captured by the old adage "two is company, three is a crowd," which suggests that the delicate dynamics of a romantic relationship may be destabilized by the addition of a third party, leading to chaos. Through rigorous analysis and numerics, we demonstrate that the intercluster phase shifts can stably coexist and exhibit different forms of chaotic behavior, including oscillatory, rotatory, and mixed-mode oscillations. We also discuss the implications of our stability results for predicting the emergence of chimeras and solitary states.
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Affiliation(s)
- Barrett N Brister
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-410, USA
| | - Vladimir N Belykh
- Department of Mathematics, Volga State University of Water Transport, 5A Nesterov street, Nizhny Novgorod 603950, Russia
- Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia
| | - Igor V Belykh
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-410, USA
- Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Avenue, Nizhny Novgorod 603950, Russia
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31
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Finite Size Effects in Networks of Coupled Neurons. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2020. [PMID: 32468555 DOI: 10.1007/978-3-030-32622-7_37] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register]
Abstract
We use extensive computer simulations to study synchronization phenomena in networks of biological neurons. Each individual neuron is modeled using the leaky integrate-and-fire (LIF) scheme, while many neurons are coupled nonlocally in a network. In this system chimera states develop, which are complex states consisting of coexisting synchronous and asynchronous network areas. We study the influence of the network size on the properties and the form of chimera states. We show that for constant coupling strength, the number of the synchronous/asynchronous domains depends quantitatively on the coupling ratio. This dependence allows to extract synchronization properties in large ensembles of neurons after extrapolating from simulations of small networks. Since computer simulations of even small neuron networks are highly demanding in memory and CPU time, this property is particularly important in view of the large number of neurons involved in any cognitive function. In total, the number of neurons in the human brain is of the order of 1010, and each of them is connected with an average of 103 other neurons.
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32
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Drauschke F, Sawicki J, Berner R, Omelchenko I, Schöll E. Effect of topology upon relay synchronization in triplex neuronal networks. CHAOS (WOODBURY, N.Y.) 2020; 30:051104. [PMID: 32491914 DOI: 10.1063/5.0008341] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2020] [Accepted: 04/20/2020] [Indexed: 06/11/2023]
Abstract
Relay synchronization in complex networks is characterized by the synchronization of remote parts of the network due to their interaction via a relay. In multilayer networks, distant layers that are not connected directly can synchronize due to signal propagation via relay layers. In this work, we investigate relay synchronization of partial synchronization patterns like chimera states in three-layer networks of interacting FitzHugh-Nagumo oscillators. We demonstrate that the phenomenon of relay synchronization is robust to topological random inhomogeneities of small-world type in the layer networks. We show that including randomness in the connectivity structure either of the remote network layers or of the relay layer increases the range of interlayer coupling strength where relay synchronization can be observed.
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Affiliation(s)
- Fenja Drauschke
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - Jakub Sawicki
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - Rico Berner
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - Iryna Omelchenko
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
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33
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Verma UK, Ambika G. Amplitude chimera and chimera death induced by external agents in two-layer networks. CHAOS (WOODBURY, N.Y.) 2020; 30:043104. [PMID: 32357668 DOI: 10.1063/5.0002457] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2020] [Accepted: 03/17/2020] [Indexed: 06/11/2023]
Abstract
We report the emergence of stable amplitude chimeras and chimera death in a two-layer network where one layer has an ensemble of identical nonlinear oscillators interacting directly through local coupling and indirectly through dynamic agents that form the second layer. The nonlocality in the interaction among the dynamic agents in the second layer induces different types of chimera-related dynamical states in the first layer. The amplitude chimeras developed in them are found to be extremely stable, while chimera death states are prevalent for increased coupling strengths. The results presented are for a system of coupled Stuart-Landau oscillators and can, in general, represent systems with short-range interactions coupled to another set of systems with long-range interactions. In this case, by tuning the range of interactions among the oscillators or the coupling strength between two types of systems, we can control the nature of chimera states and the system can also be restored to homogeneous steady states. The dynamic agents interacting nonlocally with long-range interactions can be considered as a dynamic environment or a medium interacting with the system. We indicate how the second layer can act as a reinforcement mechanism on the first layer under various possible interactions for desirable effects.
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Affiliation(s)
- Umesh Kumar Verma
- Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India
| | - G Ambika
- Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India
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34
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García RA, Martí AC, Cabeza C, Rubido N. Small-worldness favours network inference in synthetic neural networks. Sci Rep 2020; 10:2296. [PMID: 32042036 PMCID: PMC7010800 DOI: 10.1038/s41598-020-59198-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Accepted: 11/28/2019] [Indexed: 12/15/2022] Open
Abstract
A main goal in the analysis of a complex system is to infer its underlying network structure from time-series observations of its behaviour. The inference process is often done by using bi-variate similarity measures, such as the cross-correlation (CC) or mutual information (MI), however, the main factors favouring or hindering its success are still puzzling. Here, we use synthetic neuron models in order to reveal the main topological properties that frustrate or facilitate inferring the underlying network from CC measurements. Specifically, we use pulse-coupled Izhikevich neurons connected as in the Caenorhabditis elegans neural networks as well as in networks with similar randomness and small-worldness. We analyse the effectiveness and robustness of the inference process under different observations and collective dynamics, contrasting the results obtained from using membrane potentials and inter-spike interval time-series. We find that overall, small-worldness favours network inference and degree heterogeneity hinders it. In particular, success rates in C. elegans networks – that combine small-world properties with degree heterogeneity – are closer to success rates in Erdös-Rényi network models rather than those in Watts-Strogatz network models. These results are relevant to understand better the relationship between topological properties and function in different neural networks.
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Affiliation(s)
- Rodrigo A García
- Universidad de la República, Instituto de Física de Facultad de Ciencias, Montevideo, 11400, Uruguay.
| | - Arturo C Martí
- Universidad de la República, Instituto de Física de Facultad de Ciencias, Montevideo, 11400, Uruguay
| | - Cecilia Cabeza
- Universidad de la República, Instituto de Física de Facultad de Ciencias, Montevideo, 11400, Uruguay
| | - Nicolás Rubido
- Universidad de la República, Instituto de Física de Facultad de Ciencias, Montevideo, 11400, Uruguay
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35
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Kang L, Tian C, Huo S, Liu Z. A two-layered brain network model and its chimera state. Sci Rep 2019; 9:14389. [PMID: 31591418 PMCID: PMC6779761 DOI: 10.1038/s41598-019-50969-5] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2019] [Accepted: 09/23/2019] [Indexed: 01/14/2023] Open
Abstract
Based on the data of cerebral cortex, we present a two-layered brain network model of coupled neurons where the two layers represent the left and right hemispheres of cerebral cortex, respectively, and the links between the two layers represent the inter-couplings through the corpus callosum. By this model we show that abundant patterns of synchronization can be observed, especially the chimera state, depending on the parameters of system such as the coupling strengths and coupling phase. Further, we extend the model to a more general two-layered network to better understand the mechanism of the observed patterns, where each hemisphere of cerebral cortex is replaced by a highly clustered subnetwork. We find that the number of inter-couplings is another key parameter for the emergence of chimera states. Thus, the chimera states come from a matching between the structure parameters such as the number of inter-couplings and clustering coefficient etc and the dynamics parameters such as the intra-, inter-coupling strengths and coupling phase etc. A brief theoretical analysis is provided to explain the borderline of synchronization. These findings may provide helpful clues to understand the mechanism of brain functions.
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Affiliation(s)
- Ling Kang
- Department of Physics, East China Normal University, Shanghai, 200062, P.R. China
| | - Changhai Tian
- Department of Physics, East China Normal University, Shanghai, 200062, P.R. China
- School of Data Science, Tongren University, Tongren, 554300, P.R. China
| | - Siyu Huo
- Department of Physics, East China Normal University, Shanghai, 200062, P.R. China
| | - Zonghua Liu
- Department of Physics, East China Normal University, Shanghai, 200062, P.R. China.
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36
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Andreev AV, Frolov NS, Pisarchik AN, Hramov AE. Chimera state in complex networks of bistable Hodgkin-Huxley neurons. Phys Rev E 2019; 100:022224. [PMID: 31574636 DOI: 10.1103/physreve.100.022224] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2019] [Indexed: 06/10/2023]
Abstract
In this paper we study a chimera state in complex networks of bistable Hodgkin-Huxley neurons with excitatory coupling, which manifests as a termination of spiking activity of a part of interacting neurons. We provide a detailed investigation of this phenomenon in scale-free, small-world, and random networks and show that the chimera state is robust to the network topology. Nevertheless, network topological properties determine the stability of spatiotemporal states and therefore affect the excitability of the chimera state in the whole network. In particular, the scale-free network whose higher degree nodes are more stable to small perturbations is least exposed to chimera formation and exhibits an abrupt transition from a spiking to a silent regime. On the other hand, small-world and random networks are more likely to provide transitions to the chimera state.
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Affiliation(s)
- A V Andreev
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Universitetskaya, 1, Innopolis, Republic of Tatarstan, 420500, Russia
| | - N S Frolov
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Universitetskaya, 1, Innopolis, Republic of Tatarstan, 420500, Russia
| | - A N Pisarchik
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Universitetskaya, 1, Innopolis, Republic of Tatarstan, 420500, Russia
- Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Madrid, Spain
| | - A E Hramov
- Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Universitetskaya, 1, Innopolis, Republic of Tatarstan, 420500, Russia
- Saratov State Medical University, Bolshaya Kazachia st., 112, Saratov, 410012, Russia
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37
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Image Entropy for the Identification of Chimera States of Spatiotemporal Divergence in Complex Coupled Maps of Matrices. ENTROPY 2019; 21:e21050523. [PMID: 33267237 PMCID: PMC7515012 DOI: 10.3390/e21050523] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Revised: 05/17/2019] [Accepted: 05/20/2019] [Indexed: 11/26/2022]
Abstract
Complex networks of coupled maps of matrices (NCMM) are investigated in this paper. It is shown that a NCMM can evolve into two different steady states—the quiet state or the state of divergence. It appears that chimera states of spatiotemporal divergence do exist in the regions around the boundary lines separating these two steady states. It is demonstrated that digital image entropy can be used as an effective measure for the visualization of these regions of chimera states in different networks (regular, feed-forward, random, and small-world NCMM).
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38
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Bukh AV, Schöll E, Anishchenko VS. Synchronization of spiral wave patterns in two-layer 2D lattices of nonlocally coupled discrete oscillators. CHAOS (WOODBURY, N.Y.) 2019; 29:053105. [PMID: 31154795 DOI: 10.1063/1.5092352] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2019] [Accepted: 04/12/2019] [Indexed: 06/09/2023]
Abstract
The paper describes the effects of mutual and external synchronization of spiral wave structures in two coupled two-dimensional lattices of coupled discrete-time oscillators. Each lattice is given by a 2D N×N network of nonlocally coupled Nekorkin maps which model neuronal activity. We show numerically that spiral wave structures, including spiral wave chimeras, can be synchronized and establish the mechanism of the synchronization scenario. Our numerical studies indicate that when the coupling strength between the lattices is sufficiently weak, only a certain part of oscillators of the interacting networks is imperfectly synchronized, while the other part demonstrates a partially synchronous behavior. If the spatiotemporal patterns in the lattices do not include incoherent cores, imperfect synchronization is realized for most oscillators above a certain value of the coupling strength. In the regime of spiral wave chimeras, the imperfect synchronization of all oscillators cannot be achieved even for sufficiently large values of the coupling strength.
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Affiliation(s)
- A V Bukh
- Department of Physics, Saratov State University, Astrakhanskaya str. 83, Saratov 410012, Russia
| | - E Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, Berlin 10623, Germany
| | - V S Anishchenko
- Department of Physics, Saratov State University, Astrakhanskaya str. 83, Saratov 410012, Russia
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39
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Bera BK, Rakshit S, Ghosh D, Kurths J. Spike chimera states and firing regularities in neuronal hypernetworks. CHAOS (WOODBURY, N.Y.) 2019; 29:053115. [PMID: 31154769 DOI: 10.1063/1.5088833] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2019] [Accepted: 04/24/2019] [Indexed: 06/09/2023]
Abstract
A complex spatiotemporal pattern with coexisting coherent and incoherent domains in a network of identically coupled oscillators is known as a chimera state. Here, we report the emergence and existence of a novel type of nonstationary chimera pattern in a network of identically coupled Hindmarsh-Rose neuronal oscillators in the presence of synaptic couplings. The development of brain function is mainly dependent on the interneuronal communications via bidirectional electrical gap junctions and unidirectional chemical synapses. In our study, we first consider a network of nonlocally coupled neurons where the interactions occur through chemical synapses. We uncover a new type of spatiotemporal pattern, which we call "spike chimera" induced by the desynchronized spikes of the coupled neurons with the coherent quiescent state. Thereafter, imperfect traveling chimera states emerge in a neuronal hypernetwork (which is characterized by the simultaneous presence of electrical and chemical synapses). Using suitable characterizations, such as local order parameter, strength of incoherence, and velocity profile, the existence of several dynamical states together with chimera states is identified in a wide range of parameter space. We also investigate the robustness of these nonstationary chimera states together with incoherent, coherent, and resting states with respect to initial conditions by using the basin stability measurement. Finally, we extend our study for the effect of firing regularity in the observed states. Interestingly, we find that the coherent motion of the neuronal network promotes the entire system to regular firing.
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Affiliation(s)
- Bidesh K Bera
- Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India
| | - Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
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40
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Bansal K, Garcia JO, Tompson SH, Verstynen T, Vettel JM, Muldoon SF. Cognitive chimera states in human brain networks. SCIENCE ADVANCES 2019; 5:eaau8535. [PMID: 30949576 PMCID: PMC6447382 DOI: 10.1126/sciadv.aau8535] [Citation(s) in RCA: 52] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Accepted: 02/13/2019] [Indexed: 05/10/2023]
Abstract
The human brain is a complex dynamical system, and how cognition emerges from spatiotemporal patterns of regional brain activity remains an open question. As different regions dynamically interact to perform cognitive tasks, variable patterns of partial synchrony can be observed, forming chimera states. We propose that the spatial patterning of these states plays a fundamental role in the cognitive organization of the brain and present a cognitively informed, chimera-based framework to explore how large-scale brain architecture affects brain dynamics and function. Using personalized brain network models, we systematically study how regional brain stimulation produces different patterns of synchronization across predefined cognitive systems. We analyze these emergent patterns within our framework to understand the impact of subject-specific and region-specific structural variability on brain dynamics. Our results suggest a classification of cognitive systems into four groups with differing levels of subject and regional variability that reflect their different functional roles.
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Affiliation(s)
- Kanika Bansal
- Human Research and Engineering Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA
- Department of Biomedical Engineering, Columbia University, New York, NY 10027, USA
- Mathematics Department, University at Buffalo, SUNY, Buffalo, NY 14260, USA
| | - Javier O. Garcia
- Human Research and Engineering Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA
- Department of Biomedical Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Steven H. Tompson
- Human Research and Engineering Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA
- Department of Biomedical Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Timothy Verstynen
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Jean M. Vettel
- Human Research and Engineering Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA
- Department of Biomedical Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
- Department of Psychological and Brain Sciences, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
| | - Sarah F. Muldoon
- Mathematics Department, University at Buffalo, SUNY, Buffalo, NY 14260, USA
- CDSE Program and Neuroscience Program, University at Buffalo, SUNY, Buffalo, NY 14260, USA
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41
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Santos MS, Protachevicz PR, Iarosz KC, Caldas IL, Viana RL, Borges FS, Ren HP, Szezech JD, Batista AM, Grebogi C. Spike-burst chimera states in an adaptive exponential integrate-and-fire neuronal network. CHAOS (WOODBURY, N.Y.) 2019; 29:043106. [PMID: 31042937 DOI: 10.1063/1.5087129] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2018] [Accepted: 03/20/2019] [Indexed: 06/09/2023]
Abstract
Chimera states are spatiotemporal patterns in which coherence and incoherence coexist. We observe the coexistence of synchronous (coherent) and desynchronous (incoherent) domains in a neuronal network. The network is composed of coupled adaptive exponential integrate-and-fire neurons that are connected by means of chemical synapses. In our neuronal network, the chimera states exhibit spatial structures both with spike and burst activities. Furthermore, those desynchronized domains not only have either spike or burst activity, but we show that the structures switch between spikes and bursts as the time evolves. Moreover, we verify the existence of multicluster chimera states.
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Affiliation(s)
- Moises S Santos
- Department of Physics, Federal University of Paraná, 80060-000 Curitiba, PR, Brazil
| | - Paulo R Protachevicz
- Graduate in Science Program-Physics, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - Kelly C Iarosz
- Institute of Physics, University of São Paulo, 05508-900 São Paulo, SP, Brazil
| | - Iberê L Caldas
- Institute of Physics, University of São Paulo, 05508-900 São Paulo, SP, Brazil
| | - Ricardo L Viana
- Department of Physics, Federal University of Paraná, 80060-000 Curitiba, PR, Brazil
| | - Fernando S Borges
- Center for Mathematics Computation and Cognition, Federal University of ABC, 09606-045 São Bernardo do Campo, SP, Brazil
| | - Hai-Peng Ren
- Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xian University of Technology, Xi'an 710048, People's Republic of China
| | - José D Szezech
- Graduate in Science Program-Physics, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - Antonio M Batista
- Graduate in Science Program-Physics, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - Celso Grebogi
- Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
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42
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Dudkowski D, Kuznetsov NV, Mokaev TN. Chimera states and hidden attractors: Comment on "Chimera states in neuronal networks: A review" by S. Majhi, B.K. Bera, D. Ghosh, M. Perc. Phys Life Rev 2019; 28:131-133. [PMID: 30827849 DOI: 10.1016/j.plrev.2019.02.005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Accepted: 02/20/2019] [Indexed: 11/16/2022]
Affiliation(s)
- Dawid Dudkowski
- Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Nikolay V Kuznetsov
- Faculty of Mathematics and Mechanics, St. Petersburg State University, 198504 Peterhof, St. Petersburg, Russia; Department of Mathematical Information Technology, University of Jyväskylä, 40014 Jyväskylä, Finland; Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, 199178 St. Petersburg, Russia.
| | - Timur N Mokaev
- Faculty of Mathematics and Mechanics, St. Petersburg State University, 198504 Peterhof, St. Petersburg, Russia
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43
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Mikhaylenko M, Ramlow L, Jalan S, Zakharova A. Weak multiplexing in neural networks: Switching between chimera and solitary states. CHAOS (WOODBURY, N.Y.) 2019; 29:023122. [PMID: 30823738 DOI: 10.1063/1.5057418] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2018] [Accepted: 01/18/2019] [Indexed: 06/09/2023]
Abstract
We investigate spatio-temporal patterns occurring in a two-layer multiplex network of oscillatory FitzHugh-Nagumo neurons, where each layer is represented by a nonlocally coupled ring. We show that weak multiplexing, i.e., when the coupling between the layers is smaller than that within the layers, can have a significant impact on the dynamics of the neural network. We develop control strategies based on weak multiplexing and demonstrate how the desired state in one layer can be achieved without manipulating its parameters, but only by adjusting the other layer. We find that for coupling range mismatch, weak multiplexing leads to the appearance of chimera states with different shapes of the mean velocity profile for parameter ranges where they do not exist in isolation. Moreover, we show that introducing a coupling strength mismatch between the layers can suppress chimera states with one incoherent domain (one-headed chimeras) and induce various other regimes such as in-phase synchronization or two-headed chimeras. Interestingly, small intra-layer coupling strength mismatch allows to achieve solitary states throughout the whole network.
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Affiliation(s)
- Maria Mikhaylenko
- Laboratory of Solution Chemistry of Advanced Materials and Technologies, ITMO University, 9 Lomonosova Str., Saint Petersburg 197101, Russian Federation
| | - Lukas Ramlow
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, Berlin 10623, Germany
| | - Sarika Jalan
- Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, Berlin 10623, Germany
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44
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Kundu S, Bera BK, Ghosh D, Lakshmanan M. Chimera patterns in three-dimensional locally coupled systems. Phys Rev E 2019; 99:022204. [PMID: 30934225 DOI: 10.1103/physreve.99.022204] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2018] [Indexed: 06/09/2023]
Abstract
The coexistence of coherent and incoherent domains, namely the appearance of chimera states, has been studied extensively in many contexts of science and technology since the past decade, though the previous studies are mostly built on the framework of one-dimensional and two-dimensional interaction topologies. Recently, the emergence of such fascinating phenomena has been studied in a three-dimensional (3D) grid formation while considering only the nonlocal interaction. Here we study the emergence and existence of chimera patterns in a three-dimensional network of coupled Stuart-Landau limit-cycle oscillators and Hindmarsh-Rose neuronal oscillators with local (nearest-neighbor) interaction topology. The emergence of different types of spatiotemporal chimera patterns is investigated by taking two distinct nonlinear interaction functions. We provide appropriate analytical explanations in the 3D grid of the network formation and the corresponding numerical justifications are given. We extend our analysis on the basis of the Ott-Antonsen reduction approach in the case of Stuart-Landau oscillators containing infinite numbers of oscillators. Particularly, in the Hindmarsh-Rose neuronal network the existence of nonstationary chimera states is characterized by an instantaneous strength of incoherence and an instantaneous local order parameter. Besides, the condition for achieving exact neuronal synchrony is obtained analytically through a linear stability analysis. The different types of collective dynamics together with chimera states are mapped over a wide range of various parameter spaces.
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Affiliation(s)
- Srilena Kundu
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700108, India
| | - Bidesh K Bera
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700108, India
- Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140001, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700108, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620024, India
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45
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Wei Z, Parastesh F, Azarnoush H, Jafari S, Ghosh D, Perc M, Slavinec M. Nonstationary chimeras in a neuronal network. ACTA ACUST UNITED AC 2018. [DOI: 10.1209/0295-5075/123/48003] [Citation(s) in RCA: 54] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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46
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Kasatkin DV, Nekorkin VI. Synchronization of chimera states in a multiplex system of phase oscillators with adaptive couplings. CHAOS (WOODBURY, N.Y.) 2018; 28:093115. [PMID: 30278636 DOI: 10.1063/1.5031681] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2018] [Accepted: 09/06/2018] [Indexed: 06/08/2023]
Abstract
We study the interaction of chimera states in multiplex two-layer systems, where each layer represents a network of interacting phase oscillators with adaptive couplings. A feature of this study is the consideration of synchronization processes for a wide range of chimeras with essentially different properties, which are achieved due to the use of different types of coupling adaptation within isolated layers. We study the effect of forced synchronization of chimera states under unidirectional action between layers. This process is accompanied not only by changes in the frequency characteristics of the oscillators, but also by the transformation of the structure of interactions within the slave layer that become close to the properties of the master layer of the system. We show that synchronization close to identical is possible, even in the case of interaction of chimeras with essentially different structural properties (number and size of coherent clusters) formed by means of a relatively large parameter mismatch between the layers. In the case of mutual action of the layers in chimera states, we found a number of new scenarios of the multiplex system behavior along with those already known, when identical or different chimeras appear in both layers. In particular, we have shown that a fairly weak interlayer coupling can lead to suppression of the chimera state when one or both layers of the system demonstrate an incoherent state. On the contrary, a strong interlayer coupling provides a complete synchronization of the layer dynamics, accompanied by the appearance of multicluster states in the system's layers.
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Affiliation(s)
- D V Kasatkin
- Institute of Applied Physics of RAS, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia
| | - V I Nekorkin
- Institute of Applied Physics of RAS, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia
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47
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Frolov NS, Maksimenko VA, Makarov VV, Kirsanov DV, Hramov AE, Kurths J. Macroscopic chimeralike behavior in a multiplex network. Phys Rev E 2018; 98:022320. [PMID: 30253535 DOI: 10.1103/physreve.98.022320] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2018] [Indexed: 06/08/2023]
Abstract
In this paper we study the dynamics of a multiplex multilayer network, where each layer is composed of identical Kuramoto-Sakaguchi phase oscillators with nonlocal coupling. We focus on a three-layer multiplex network and observe a specific form of multiplex network behavior, the macroscopic chimeralike state. It is decomposed by a splitting of the layers with initially close dynamics into subgroups. The first group consists of two layers performing one type of dynamics, whereas the rest perform the other type, after the introduction of interlayer coupling. Based on an intensive computational analysis, we show that areas of macroscopic chimeralike states are observed close to the critical transition points of intralayer (microscopic) states in the parameter space. We find that this macroscopic chimeralike state is excited at weak and medium interlayer coupling strength, wherein the interlayer phase lag here plays an important role, since this is a network parameter which controls macroscopic dynamics and transforms boundaries between intralayer states. The obtained numerical results are validated analytically by considering the multiplex network dynamics using the Ott-Antonsen reduction of the governing network equations.
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Affiliation(s)
- Nikita S Frolov
- Research and Educational Center "Artificial Intelligence Systems and Neurotechnology," Yuri Gagarin State Technical University of Saratov, Saratov 410054, Russia
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
| | - Vladimir A Maksimenko
- Research and Educational Center "Artificial Intelligence Systems and Neurotechnology," Yuri Gagarin State Technical University of Saratov, Saratov 410054, Russia
| | - Vladimir V Makarov
- Research and Educational Center "Artificial Intelligence Systems and Neurotechnology," Yuri Gagarin State Technical University of Saratov, Saratov 410054, Russia
| | - Daniil V Kirsanov
- Research and Educational Center "Artificial Intelligence Systems and Neurotechnology," Yuri Gagarin State Technical University of Saratov, Saratov 410054, Russia
| | - Alexander E Hramov
- Research and Educational Center "Artificial Intelligence Systems and Neurotechnology," Yuri Gagarin State Technical University of Saratov, Saratov 410054, Russia
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
- Department of Physics, Humboldt University, 12489 Berlin, Germany
- Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
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48
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Majhi S, Ghosh D. Alternating chimeras in networks of ephaptically coupled bursting neurons. CHAOS (WOODBURY, N.Y.) 2018; 28:083113. [PMID: 30180636 DOI: 10.1063/1.5022612] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2018] [Accepted: 07/26/2018] [Indexed: 06/08/2023]
Abstract
The distinctive phenomenon of the chimera state has been explored in neuronal systems under a variety of different network topologies during the last decade. Nevertheless, in all the works, the neurons are presumed to interact with each other directly with the help of synapses only. But, the influence of ephaptic coupling, particularly magnetic flux across the membrane, is mostly unexplored and should essentially be dealt with during the emergence of collective electrical activities and propagation of signals among the neurons in a network. Through this article, we report the development of an emerging dynamical state, namely, the alternating chimera, in a network of identical neuronal systems induced by an external electromagnetic field. Owing to this interaction scenario, the nonlinear neuronal oscillators are coupled indirectly via electromagnetic induction with magnetic flux, through which neurons communicate in spite of the absence of physical connections among them. The evolution of each neuron, here, is described by the three-dimensional Hindmarsh-Rose dynamics. We demonstrate that the presence of such non-locally and globally interacting external environments induces a stationary alternating chimera pattern in the ensemble of neurons, whereas in the local coupling limit, the network exhibits a transient chimera state whenever the local dynamics of the neurons is of the chaotic square-wave bursting type. For periodic square-wave bursting of the neurons, a similar qualitative phenomenon has been witnessed with the exception of the disappearance of cluster states for non-local and global interactions. Besides these observations, we advance our work while providing confirmation of the findings for neuronal ensembles exhibiting plateau bursting dynamics and also put forward the fact that the plateau pattern actually favors the alternating chimera more than others. These results may deliver better interpretations for different aspects of synchronization appearing in a network of neurons through field coupling that also relaxes the prerequisite of synaptic connectivity for realizing the chimera state in neuronal networks.
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Affiliation(s)
- Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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49
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Malchow AK, Omelchenko I, Schöll E, Hövel P. Robustness of chimera states in nonlocally coupled networks of nonidentical logistic maps. Phys Rev E 2018; 98:012217. [PMID: 30110780 DOI: 10.1103/physreve.98.012217] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2018] [Indexed: 06/08/2023]
Abstract
We investigate the dynamics of nonlocally coupled time-discrete maps with emphasis on the occurrence and robustness of chimera states. These peculiar, hybrid states are characterized by a coexistence of coherent and incoherent regions. We consider logistic maps coupled on a one-dimensional ring with finite coupling radius. Domains of chimera existence form different tongues in the parameter space of coupling range and coupling strength. For a sufficiently large coupling strength, each tongue refers to a wave number describing the structure of the spatial profile. We also analyze the period-adding scheme within these tongues and multiplicity of period solutions. Furthermore, we study the robustness of chimeras with respect to parameter inhomogeneities and find that these states persist for different widths of the parameter distribution. Finally, we explore the spatial structure of the chimera using a spatial correlation function.
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Affiliation(s)
- Anne-Kathleen Malchow
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Iryna Omelchenko
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Philipp Hövel
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu Berlin, Philippstraße 13, 10115 Berlin, Germany
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50
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Kasimatis T, Hizanidis J, Provata A. Three-dimensional chimera patterns in networks of spiking neuron oscillators. Phys Rev E 2018; 97:052213. [PMID: 29906870 DOI: 10.1103/physreve.97.052213] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2018] [Indexed: 06/08/2023]
Abstract
We study the stable spatiotemporal patterns that arise in a three-dimensional (3D) network of neuron oscillators, whose dynamics is described by the leaky integrate-and-fire (LIF) model. More specifically, we investigate the form of the chimera states induced by a 3D coupling matrix with nonlocal topology. The observed patterns are in many cases direct generalizations of the corresponding two-dimensional (2D) patterns, e.g., spheres, layers, and cylinder grids. We also find cylindrical and "cross-layered" chimeras that do not have an equivalent in 2D systems. Quantitative measures are calculated, such as the ratio of synchronized and unsynchronized neurons as a function of the coupling range, the mean phase velocities, and the distribution of neurons in mean phase velocities. Based on these measures, the chimeras are categorized in two families. The first family of patterns is observed for weaker coupling and exhibits higher mean phase velocities for the unsynchronized areas of the network. The opposite holds for the second family, where the unsynchronized areas have lower mean phase velocities. The various measures demonstrate discontinuities, indicating criticality as the parameters cross from the first family of patterns to the second.
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Affiliation(s)
- T Kasimatis
- Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos," 15310 Athens, Greece
- School of Applied Mathematical and Physical Sciences, National Technical University of Athens, 15780 Athens, Greece
| | - J Hizanidis
- Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos," 15310 Athens, Greece
- Department of Physics, University of Crete, 71003 Heraklion, Greece
- National University of Science and Technology MISiS, Leninsky Prospect 4, Moscow, 119049, Russia
| | - A Provata
- Institute of Nanoscience and Nanotechnology, National Center for Scientific Research "Demokritos," 15310 Athens, Greece
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