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Rybalova E, Nikishina N, Strelkova G. Controlling spatiotemporal dynamics of neural networks by Lévy noise. CHAOS (WOODBURY, N.Y.) 2024; 34:041103. [PMID: 38648383 DOI: 10.1063/5.0206094] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/29/2024] [Accepted: 04/04/2024] [Indexed: 04/25/2024]
Abstract
We explore numerically how additive Lévy noise influences the spatiotemporal dynamics of a neural network of nonlocally coupled FitzHugh-Nagumo oscillators. Without noise, the network can exhibit various partial or cluster synchronization patterns, such as chimera and solitary states, which can also coexist in the network for certain values of the control parameters. Our studies show that these structures demonstrate different responses to additive Lévy noise and, thus, the dynamics of the neural network can be effectively controlled by varying the scale parameter and the stability index of Lévy noise. Specifically, introducing Lévy noise in the multistability mode can increase the probability of observing chimera states while suppressing solitary states. Nonetheless, decreasing the stability parameter enables one to diminish the noise effect on chimera states and amplify it on solitary states.
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Affiliation(s)
- E Rybalova
- Institute of Physics, Radiophysics and Nonlinear Dynamics Departament, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - N Nikishina
- Institute of Physics, Radiophysics and Nonlinear Dynamics Departament, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - G Strelkova
- Institute of Physics, Radiophysics and Nonlinear Dynamics Departament, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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2
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Fateev I, Polezhaev A. Chimera states in a chain of superdiffusively coupled neurons. CHAOS (WOODBURY, N.Y.) 2023; 33:103110. [PMID: 37831792 DOI: 10.1063/5.0168422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 09/19/2023] [Indexed: 10/15/2023]
Abstract
Two- and three-component systems of superdiffusion equations describing the dynamics of action potential propagation in a chain of non-locally interacting neurons with Hindmarsh-Rose nonlinear functions have been considered. Non-local couplings based on the fractional Laplace operator describing superdiffusion kinetics are found to support chimeras. In turn, the system with local couplings, based on the classical Laplace operator, shows synchronous behavior. For several parameters responsible for the activation properties of neurons, it is shown that the structure and evolution of chimera states depend significantly on the fractional Laplacian exponent, reflecting non-local properties of the couplings. For two-component systems, an anisotropic transition to full incoherence in the parameter space responsible for non-locality of the first and second variables is established. Introducing a third slow variable induces a gradual transition to incoherence via additional chimera states formation. We also discuss the possible causes of chimera states formation in such a system of non-locally interacting neurons and relate them with the properties of the fractional Laplace operator in a system with global coupling.
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Affiliation(s)
- I Fateev
- P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskiy Prospekt, Moscow 119991, Russian Federation
| | - A Polezhaev
- P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskiy Prospekt, Moscow 119991, Russian Federation
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3
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Rybalova E, Nechaev V, Schöll E, Strelkova G. Chimera resonance in networks of chaotic maps. CHAOS (WOODBURY, N.Y.) 2023; 33:093138. [PMID: 37748485 DOI: 10.1063/5.0164008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 09/05/2023] [Indexed: 09/27/2023]
Abstract
We explore numerically the impact of additive Gaussian noise on the spatiotemporal dynamics of ring networks of nonlocally coupled chaotic maps. The local dynamics of network nodes is described by the logistic map, the Ricker map, and the Henon map. 2D distributions of the probability of observing chimera states are constructed in terms of the coupling strength and the noise intensity and for several choices of the local dynamics parameters. It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance.
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Affiliation(s)
- Elena Rybalova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - Vasilii Nechaev
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, 10115 Berlin, Germany
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
| | - Galina Strelkova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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4
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Mbouna SGN, Banerjee T, Schöll E. Chimera patterns with spatial random swings between periodic attractors in a network of FitzHugh-Nagumo oscillators. Phys Rev E 2023; 107:054204. [PMID: 37329071 DOI: 10.1103/physreve.107.054204] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 04/21/2023] [Indexed: 06/18/2023]
Abstract
For the study of symmetry-breaking phenomena in neuronal networks, simplified versions of the FitzHugh-Nagumo model are widely used. In this paper, these phenomena are investigated in a network of FitzHugh-Nagumo oscillators taken in the form of the original model and it is found that it exhibits diverse partial synchronization patterns that are unobserved in the networks with simplified models. Apart from the classical chimera, we report a new type of chimera pattern whose incoherent clusters are characterized by spatial random swings among a few fixed periodic attractors. Another peculiar hybrid state is found that combines the features of this chimera state and a solitary state such that the main coherent cluster is interspersed with some nodes with identical solitary dynamics. In addition, oscillation death including chimera death emerges in this network. A reduced model of the network is derived to study oscillation death, which helps explaining the transition from spatial chaos to oscillation death via the chimera state with a solitary state. This study deepens our understanding of chimera patterns in neuronal networks.
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Affiliation(s)
- S G Ngueuteu Mbouna
- Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaoundé I, P. O. Box 812, Yaoundé, Cameroon
| | - Tanmoy Banerjee
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, India
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany; Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany; and Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, 10115 Berlin, Germany
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5
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Ragavan A, Manoranjani M, Senthilkumar DV, Chandrasekar VK. Multistable chimera states in a smallest population of three coupled oscillators. Phys Rev E 2023; 107:044209. [PMID: 37198793 DOI: 10.1103/physreve.107.044209] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 03/28/2023] [Indexed: 05/19/2023]
Abstract
We uncover the emergence of distinct sets of multistable chimera states in addition to chimera death and synchronized states in a smallest population of three globally coupled oscillators with mean-field diffusive coupling. Sequence of torus bifurcations result in the manifestation of distinct periodic orbits as a function of the coupling strength, which in turn result in the genesis of distinct chimera states constituted by two synchronized oscillators coexisting with an asynchronous oscillator. Two subsequent Hopf bifurcations result in homogeneous and inhomogeneous steady states resulting in desynchronized steady states and chimera death state among the coupled oscillators. The periodic orbits and the steady states lose their stability via a sequence of saddle-loop and saddle-node bifurcations finally resulting in a stable synchronized state. We have generalized these results to N coupled oscillators and also deduced the variational equations corresponding to the perturbation transverse to the synchronization manifold and corroborated the synchronized state in the two-parameter phase diagrams using its largest eigenvalue. Chimera states in three coupled oscillators emerge as a solitary state in N coupled oscillator ensemble.
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Affiliation(s)
- A Ragavan
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
| | - M Manoranjani
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
| | - D V Senthilkumar
- School of Physics,Indian Institute of Science Education and Research, Thiruvananthapuram-695551, Kerala, India
| | - V K Chandrasekar
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
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6
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Rybalova E, Muni S, Strelkova G. Transition from chimera/solitary states to traveling waves. CHAOS (WOODBURY, N.Y.) 2023; 33:033104. [PMID: 37003811 DOI: 10.1063/5.0138207] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Accepted: 02/08/2023] [Indexed: 06/19/2023]
Abstract
We study numerically the spatiotemporal dynamics in a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. It is shown that the discretized oscillator exhibits richer behavior, combining the peculiarities of both the original system and its own dynamics. Moreover, a large variety of spatiotemporal structures is observed in the network of discrete van der Pol oscillators when the discretization parameter and the coupling strength are varied. Regimes, such as the coexistence of a multichimera state/a traveling wave and a solitary state are revealed for the first time and are studied in detail. It is established that the majority of the observed chimera/solitary states, including the newly found ones, are transient toward a purely traveling wave mode. The peculiarities of the transition process and the lifetime (transient duration) of the chimera structures and the solitary state are analyzed depending on the system parameters, the observation time, initial conditions, and the influence of external noise.
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Affiliation(s)
- E Rybalova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - S Muni
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Campus Road, Mohanpur, West Bengal 741246, India
| | - G Strelkova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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7
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Schülen L, Gerdes A, Wolfrum M, Zakharova A. Solitary routes to chimera states. Phys Rev E 2022; 106:L042203. [PMID: 36397505 DOI: 10.1103/physreve.106.l042203] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 09/26/2022] [Indexed: 06/16/2023]
Abstract
We show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit we demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. We demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators.
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Affiliation(s)
- Leonhard Schülen
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Alexander Gerdes
- Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany
| | - Matthias Wolfrum
- Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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Mihara A, Medeiros ES, Zakharova A, Medrano-T RO. Sparsity-driven synchronization in oscillator networks. CHAOS (WOODBURY, N.Y.) 2022; 32:033114. [PMID: 35364836 DOI: 10.1063/5.0074008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2021] [Accepted: 02/24/2022] [Indexed: 06/14/2023]
Abstract
The emergence of synchronized behavior is a direct consequence of networking dynamical systems. Naturally, strict instances of this phenomenon, such as the states of complete synchronization, are favored or even ensured in networks with a high density of connections. Conversely, in sparse networks, the system state-space is often shared by a variety of coexistent solutions. Consequently, the convergence to complete synchronized states is far from being certain. In this scenario, we report the surprising phenomenon in which completely synchronized states are made the sole attractor of sparse networks by removing network links, the sparsity-driven synchronization. This phenomenon is observed numerically for nonlocally coupled Kuramoto networks and verified analytically for locally coupled ones. In addition, we unravel the bifurcation scenario underlying the network transition to completely synchronized behavior. Furthermore, we present a simple procedure, based on the bifurcations in the thermodynamic limit, that determines the minimum number of links to be removed in order to ensure complete synchronization. Finally, we propose an application of the reported phenomenon as a control scheme to drive complete synchronization in high connectivity networks.
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Affiliation(s)
- Antonio Mihara
- Departamento de Física, Universidade Federal de São Paulo, UNIFESP, Campus Diadema, 09913-030 São Paulo, Brasil
| | - Everton S Medeiros
- Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, 26111 Oldenburg, Germany
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Rene O Medrano-T
- Departamento de Física, Universidade Federal de São Paulo, UNIFESP, Campus Diadema, 09913-030 São Paulo, Brasil
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9
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Rybalova E, Strelkova G. Response of solitary states to noise-modulated parameters in nonlocally coupled networks of Lozi maps. CHAOS (WOODBURY, N.Y.) 2022; 32:021101. [PMID: 35232034 DOI: 10.1063/5.0082431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Accepted: 01/20/2022] [Indexed: 06/14/2023]
Abstract
We study numerically the impact of heterogeneity in parameters on the dynamics of nonlocally coupled discrete-time systems, which exhibit solitary states along the transition from coherence to incoherence. These partial synchronization patterns are described as states when single or several elements demonstrate different dynamics compared with the behavior of other elements in a network. Using as an example a ring network of nonlocally coupled Lozi maps, we explore the robustness of solitary states to heterogeneity in parameters of local dynamics or coupling strength. It is found that if these network parameters are continuously modulated by noise, solitary states are suppressed as the noise intensity increases. However, these states may persist in the case of static randomly distributed system parameters for a wide range of the distribution width. Domains of solitary state existence are constructed in the parameter plane of coupling strength and noise intensity using a cross-correlation coefficient.
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Affiliation(s)
- Elena Rybalova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - Galina Strelkova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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10
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A New Memristive Neuron Map Model and Its Network’s Dynamics under Electrochemical Coupling. ELECTRONICS 2022. [DOI: 10.3390/electronics11010153] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
A memristor is a vital circuit element that can mimic biological synapses. This paper proposes the memristive version of a recently proposed map neuron model based on the phase space. The dynamic of the memristive map model is investigated by using bifurcation and Lyapunov exponents’ diagrams. The results prove that the memristive map can present different behaviors such as spiking, periodic bursting, and chaotic bursting. Then, a ring network is constructed by hybrid electrical and chemical synapses, and the memristive neuron models are used to describe the nodes. The collective behavior of the network is studied. It is observed that chemical coupling plays a crucial role in synchronization. Different kinds of synchronization, such as imperfect synchronization, complete synchronization, solitary state, two-cluster synchronization, chimera, and nonstationary chimera, are identified by varying the coupling strengths.
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11
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Franović I, Eydam S, Semenova N, Zakharova A. Unbalanced clustering and solitary states in coupled excitable systems. CHAOS (WOODBURY, N.Y.) 2022; 32:011104. [PMID: 35105111 DOI: 10.1063/5.0077022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Accepted: 12/28/2021] [Indexed: 06/14/2023]
Abstract
We discover the mechanisms of emergence and the link between two types of symmetry-broken states, the unbalanced periodic two-cluster states and solitary states, in coupled excitable systems with attractive and repulsive interactions. The prevalent solitary states in non-locally coupled arrays, whose self-organization is based on successive (order preserving) spiking of units, derive their dynamical features from the corresponding unbalanced cluster states in globally coupled networks. Apart from the states with successive spiking, we also find cluster and solitary states where the interplay of excitability and local multiscale dynamics gives rise to so-called leap-frog activity patterns with an alternating order of spiking between the units. We show that the noise affects the system dynamics by suppressing the multistability of cluster states and by inducing pattern homogenization, transforming solitary states into patterns of patched synchrony.
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Affiliation(s)
- Igor Franović
- Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Sebastian Eydam
- Neural Circuits and Computations Unit, RIKEN Center for Brain Science, 2-1 Hirosawa, 351-0106 Wako, Japan
| | - Nadezhda Semenova
- Institute of Physics and Department of Fundamental Medicine and Medical Technology, Saratov State University, Astrakhanskaya str. 83, Saratov 410012, Russia
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
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12
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Cenk Eser M, Medeiros ES, Riza M, Zakharova A. Edges of inter-layer synchronization in multilayer networks with time-switching links. CHAOS (WOODBURY, N.Y.) 2021; 31:103119. [PMID: 34717318 DOI: 10.1063/5.0065310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 09/29/2021] [Indexed: 06/13/2023]
Abstract
We investigate the transition to synchronization in a two-layer network of oscillators with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the timescale of topological changes. Initially, we observe a smooth transition to complete synchronization for the static inter-layer topology by increasing the number of inter-layer links. Next, for a dynamic topology with the existent inter-layer links randomly changing among identical oscillators in the layers, we observe a significant improvement in the system synchronizability; i.e., the layers synchronize with lower inter-layer connectivity. More interestingly, we find that, for a critical switching time, the transition from the network state of low inter-layer synchronization to high inter-layer synchronization occurs abruptly as the number of inter-layer links increases. We interpret this phenomenon as shrinking and ultimately the disappearance of the basin of attraction of a desynchronized network state.
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Affiliation(s)
- Muhittin Cenk Eser
- Department of Physics, Eastern Mediterranean University, 99628 Famagusta, North Cyprus, via Mersin 10, Turkey
| | - Everton S Medeiros
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Mustafa Riza
- Department of Physics, Eastern Mediterranean University, 99628 Famagusta, North Cyprus, via Mersin 10, Turkey
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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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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14
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Goldobin DS. Mean-field models of populations of quadratic integrate-and-fire neurons with noise on the basis of the circular cumulant approach. CHAOS (WOODBURY, N.Y.) 2021; 31:083112. [PMID: 34470229 DOI: 10.1063/5.0061575] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2021] [Accepted: 07/20/2021] [Indexed: 06/13/2023]
Abstract
We develop a circular cumulant representation for the recurrent network of quadratic integrate-and-fire neurons subject to noise. The synaptic coupling is global or macroscopically equivalent to it. We assume a Lorentzian distribution of the parameter controlling whether the isolated individual neuron is periodically spiking or excitable. For the infinite chain of circular cumulant equations, a hierarchy of smallness is identified; on the basis of it, we truncate the chain and suggest several two-cumulant neural mass models. These models allow one to go beyond the Ott-Antonsen Ansatz and describe the effect of noise on hysteretic transitions between macroscopic regimes of a population with inhibitory coupling. The accuracy of two-cumulant models is analyzed in detail.
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Affiliation(s)
- Denis S Goldobin
- Institute of Continuous Media Mechanics, UB RAS, Academician Korolev Street 1, 614013 Perm, Russia
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15
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Sawicki J, Koulen JM, Schöll E. Synchronization scenarios in three-layer networks with a hub. CHAOS (WOODBURY, N.Y.) 2021; 31:073131. [PMID: 34340334 DOI: 10.1063/5.0055835] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Accepted: 06/22/2021] [Indexed: 06/13/2023]
Abstract
We study various relay synchronization scenarios in a three-layer network, where the middle (relay) layer is a single node, i.e., a hub. The two remote layers consist of non-locally coupled rings of FitzHugh-Nagumo oscillators modeling neuronal dynamics. All nodes of the remote layers are connected to the hub. The role of the hub and its importance for the existence of chimera states are investigated in dependence on the inter-layer coupling strength and inter-layer time delay. Tongue-like regions in the parameter plane exhibiting double chimeras, i.e., chimera states in the remote layers whose coherent cores are synchronized with each other, and salt-and-pepper states are found. At very low intra-layer coupling strength, when chimera states do not exist in single layers, these may be induced by the hub. Also, the influence of the dilution of links between the remote layers and the hub upon the dynamics is investigated. The greatest effect of dilution is observed when links to the coherent domain of the chimeras are removed.
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Affiliation(s)
- Jakub Sawicki
- Potsdam Institute for Climate Impact Research, Telegrafenberg A, 31, 14473 Potsdam, Germany
| | - Julia M Koulen
- Potsdam Institute for Climate Impact Research, Telegrafenberg A, 31, 14473 Potsdam, Germany
| | - Eckehard Schöll
- Potsdam Institute for Climate Impact Research, Telegrafenberg A, 31, 14473 Potsdam, Germany
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16
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Rakshit S, Majhi S, Kurths J, Ghosh D. Neuronal synchronization in long-range time-varying networks. CHAOS (WOODBURY, N.Y.) 2021; 31:073129. [PMID: 34340354 DOI: 10.1063/5.0057276] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 06/21/2021] [Indexed: 06/13/2023]
Abstract
We study synchronization in neuronal ensembles subject to long-range electrical gap junctions which are time-varying. As a representative example, we consider Hindmarsh-Rose neurons interacting based upon temporal long-range connections through electrical couplings. In particular, we adopt the connections associated with the direct 1-path network to form a small-world network and follow-up with the corresponding long-range network. Further, the underlying direct small-world network is allowed to temporally change; hence, all long-range connections are also temporal, which makes the model much more realistic from the neurological perspective. This time-varying long-range network is formed by rewiring each link of the underlying 1-path network stochastically with a characteristic rewiring probability pr, and accordingly all indirect k(>1)-path networks become temporal. The critical interaction strength to reach complete neuronal synchrony is much lower when we take up rapidly switching long-range interactions. We employ the master stability function formalism in order to characterize the local stability of the state of synchronization. The analytically derived stability condition for the complete synchrony state agrees well with the numerical results. Our work strengthens the understanding of time-varying long-range interactions in neuronal ensembles.
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Affiliation(s)
- Sarbendu Rakshit
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research - Telegraphenberg A 31, Potsdam 14473, Germany
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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17
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Frisman EY, Zhdanova OL, Kulakov MP, Neverova GP, Revutskaya OL. Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part II. BIOL BULL+ 2021. [DOI: 10.1134/s1062359021030055] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Shepelev IA, Muni SS, Vadivasova TE. Spatiotemporal patterns in a 2D lattice with linear repulsive and nonlinear attractive coupling. CHAOS (WOODBURY, N.Y.) 2021; 31:043136. [PMID: 34251249 DOI: 10.1063/5.0048324] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 04/07/2021] [Indexed: 06/13/2023]
Abstract
We explore the emergence of a variety of different spatiotemporal patterns in a 2D lattice of self-sustained oscillators, which interact nonlocally through an active nonlinear element. A basic element is a van der Pol oscillator in a regime of relaxation oscillations. The active nonlinear coupling can be implemented by a radiophysical element with negative resistance in its current-voltage curve taking into account nonlinear characteristics (for example, a tunnel diode). We show that such coupling consists of two parts, namely, a repulsive linear term and an attractive nonlinear term. This interaction leads to the emergence of only standing waves with periodic dynamics in time and absence of any propagating wave processes. At the same time, many different spatiotemporal patterns occur when the coupling parameters are varied, namely, regular and complex cluster structures, such as chimera states. This effect is associated with the appearance of new periodic states of individual oscillators by the repulsive part of coupling, while the attractive term attenuates this effect. We also show influence of the coupling nonlinearity on the spatiotemporal dynamics.
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Affiliation(s)
- I A Shepelev
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - S S Muni
- School of Fundamental Sciences, Massey University, Palmerston North, New Zealand
| | - T E Vadivasova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
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Bahramian A, Parastesh F, Pham VT, Kapitaniak T, Jafari S, Perc M. Collective behavior in a two-layer neuronal network with time-varying chemical connections that are controlled by a Petri net. CHAOS (WOODBURY, N.Y.) 2021; 31:033138. [PMID: 33810759 DOI: 10.1063/5.0045840] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Accepted: 03/02/2021] [Indexed: 06/12/2023]
Abstract
In this paper, we propose and study a two-layer network composed of a Petri net in the first layer and a ring of coupled Hindmarsh-Rose neurons in the second layer. Petri nets are appropriate platforms not only for describing sequential processes but also for modeling information circulation in complex systems. Networks of neurons, on the other hand, are commonly used to study synchronization and other forms of collective behavior. Thus, merging both frameworks into a single model promises fascinating new insights into neuronal collective behavior that is subject to changes in network connectivity. In our case, the Petri net in the first layer manages the existence of excitatory and inhibitory links among the neurons in the second layer, thereby making the chemical connections time-varying. We focus on the emergence of different types of collective behavior in the model, such as synchronization, chimeras, and solitary states, by considering different inhibitory and excitatory tokens in the Petri net. We find that the existence of only inhibitory or excitatory tokens disturbs the synchronization of electrically coupled neurons and leads toward chimera and solitary states.
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Affiliation(s)
- Alireza Bahramian
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave., Valiasr Square, Tehran 159163-4311, Iran
| | - Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave., Valiasr Square, Tehran 159163-4311, Iran
| | - Viet-Thanh Pham
- Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Sajad Jafari
- Center for Computational Biology, Chennai Institute of Technology, Chennai, Tamil Nadu 600069, India
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
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