1
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Qian Y, Han J, Yang R, Chen W, Lei Z, Zheng Z. Emergence of chimeralike oscillation modes in excitable complex networks with preferentially cutting-rewiring operation. CHAOS (WOODBURY, N.Y.) 2024; 34:063143. [PMID: 38934725 DOI: 10.1063/5.0167251] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Accepted: 06/05/2024] [Indexed: 06/28/2024]
Abstract
In this paper, the preferentially cutting-rewiring operation (PCRO) consisting of the cutting procedure and the rewiring procedure is proposed and is applied on an excitable Erdös-Rényi random network (EERRN), by which the structure of the initially homogeneous network changes dramatically, and lots of common leaves (CLs) are formed between the two hubs. Subsequently, besides the single-mode oscillations that can be usually observed in homogeneous excitable systems, a new kind of multi-mode oscillations composed of synchronous and asynchronous parts can self-organize to emerge, which are similar to the coherent and incoherent clusters in traditional chimera states and are consequently named as the chimeralike oscillation modes (CLOMs). Importantly, by utilizing the dominant phase-advanced driving method, both the mechanisms for the formation and the emergence of CLOMs in EERRNs with PCRO are well explained, among which the CL is exposed to play a key role in forming the CLOMs. Furthermore, the PCRO-induced CLOM phenomena can also be observed in other paradigmatic network models or with other paradigmatic excitable dynamics, which definitely confirms that the PCRO is an universal method in inducing the CLOMs in excitable complex networks. Our contributions may shed lights on a new perspective of the emergence of CLOMs in complex systems and would have great impacts in related fields.
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Affiliation(s)
- Yu Qian
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Jing Han
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Runru Yang
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Wentao Chen
- School of Systems Science, Beijing Normal University, Beijing 100875, China
| | - Zhao Lei
- College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721007, China
| | - Zhigang Zheng
- Institute of Systems Science, Huaqiao University, Xiamen 361021, China
- College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
- School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
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2
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Bollt E, Fish J, Kumar A, Roque Dos Santos E, Laurienti PJ. Fractal basins as a mechanism for the nimble brain. Sci Rep 2023; 13:20860. [PMID: 38012212 PMCID: PMC10682042 DOI: 10.1038/s41598-023-45664-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 10/22/2023] [Indexed: 11/29/2023] Open
Abstract
An interesting feature of the brain is its ability to respond to disparate sensory signals from the environment in unique ways depending on the environmental context or current brain state. In dynamical systems, this is an example of multi-stability, the ability to switch between multiple stable states corresponding to specific patterns of brain activity/connectivity. In this article, we describe chimera states, which are patterns consisting of mixed synchrony and incoherence, in a brain-inspired dynamical systems model composed of a network with weak individual interactions and chaotic/periodic local dynamics. We illustrate the mechanism using synthetic time series interacting on a realistic anatomical brain network derived from human diffusion tensor imaging. We introduce the so-called vector pattern state (VPS) as an efficient way of identifying chimera states and mapping basin structures. Clustering similar VPSs for different initial conditions, we show that coexisting attractors of such states reveal intricately "mingled" fractal basin boundaries that are immediately reachable. This could explain the nimble brain's ability to rapidly switch patterns between coexisting attractors.
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Affiliation(s)
- Erik Bollt
- Department of Electrical and Computer Engineering, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA.
- Clarkson Center for Complex Systems Science, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA.
| | - Jeremie Fish
- Department of Electrical and Computer Engineering, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
- Clarkson Center for Complex Systems Science, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
| | - Anil Kumar
- Department of Electrical and Computer Engineering, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
- Clarkson Center for Complex Systems Science, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
| | - Edmilson Roque Dos Santos
- Department of Electrical and Computer Engineering, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
- Clarkson Center for Complex Systems Science, Clarkson University, 8 Clarkson Ave., Potsdam, NY, 13699, USA
- Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, Av. Trab. São Carlense, 400, São Carlos, SP, 13566-590, Brazil
| | - Paul J Laurienti
- Department of Radiology, Wake Forest University School of Medicine, 475 Vine Street, Winston-Salem, NC, 27101, USA
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3
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Feng P, Yang J, Wu Y. Chimera state in a feed-forward neuronal network. Cogn Neurodyn 2023; 17:1119-1130. [PMID: 37790707 PMCID: PMC10542440 DOI: 10.1007/s11571-022-09928-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2022] [Revised: 06/10/2022] [Accepted: 06/13/2022] [Indexed: 01/11/2023] Open
Abstract
Feed-forward effect gives rise to synchronization in neuron firing in deep layers of multiple neuronal network. But complete synchronization means the loss of encoding ability. In order to avoid the contradiction, we ask whether partial synchronization (coexistence of disordered and synchronized neuron firing emerges, also called chimera state) as a compromise strategy can achieve in the feed-forward multiple-layer network. The answer is YES. In order to manifest our argument, we design a multi-layer neuronal network in which neurons in every layer are arranged in a ring topology and neuron firing propagates within (intra-) and across (inter-) the multiply layers. Emergence of chimera state and other patterns highly depends on initial condition of neuronal network and strength of feed-forward effect. Chimera state, cluster and synchronization intra- and inter- layers are displayed by sequence through layers when initial values are elaborately chosen to guarantee emergence of chimera state in the first layer. All type of patterns except chimera state propagates down toward deeper layers in different speeds varying with strength of feed-forward effect. If chimera state already exists in every layer, feed-forward effect with strong and moderate strength spoils chimera states in deep layers and they can only survive in first few layers. When the effect is small enough, chimera states will propagate down toward deeper layers. Indeed, chimera states could exist and transit to deeper layers in a regular multiple network under very strict conditions. The results help understanding better the neuron firing propagating and encoding scheme in a feed-forward neuron network.
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Affiliation(s)
- Peihua Feng
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, 710049 People’s Republic of China
| | - Jiayi Yang
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, 710049 People’s Republic of China
| | - Ying Wu
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, 710049 People’s Republic of China
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4
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Kang L, Liu Z. Unraveling the complexity of neural networks: Comment on "Structure and function in artificial, zebrafish and human neural networks" by Peng Ji et al. Phys Life Rev 2023; 46:158-160. [PMID: 37442034 DOI: 10.1016/j.plrev.2023.07.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 07/03/2023] [Indexed: 07/15/2023]
Affiliation(s)
- Ling Kang
- School of Physics and Electronic Science, East China Normal University, Shanghai, 200241, PR China; Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, 200433, PR China
| | - Zonghua Liu
- School of Physics and Electronic Science, East China Normal University, Shanghai, 200241, PR China.
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5
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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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6
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Feng P, Yang J, Wu Y, Liu Z. Alternating chimera states in complex networks with modular structures. CHAOS (WOODBURY, N.Y.) 2023; 33:033136. [PMID: 37003804 DOI: 10.1063/5.0132072] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 02/28/2023] [Indexed: 06/19/2023]
Abstract
Chimera, the coexistence state of synchronization and non-synchronization, widely exists in complex networks. It has a great potentially explanatory power for the unihemispheric sleep of birds and some mammals, in which the synchronizations of the hemispheres of the cerebral cortex are evolving alternately. In this study, a coupled nonlinear oscillator system with a topology of the modular complex network was constructed to simulate the left and right hemispheres of the brain. The results showed that a stable chimera, an alternating chimera, and a breathing chimera were produced when the coupling strength and connection probability of the left and right hemispheres were changed. Further, we studied the effect of noise on rich synchronous patterns and found that the alternating chimera was robust to Gaussian white noise when the strength was not very large. Finally, our study was extended to a complex network with three sub-networks, and an alternating chimera could exist in two or three sub-networks. Our research provides a deeper insight into the mechanism of brain function like unihemispheric sleep.
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Affiliation(s)
- Peihua Feng
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
| | - Jiayi Yang
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
| | - Ying Wu
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
| | - Zhilong Liu
- Hefei General Machinery Research Institute, State Key Laboratory of Compressor Technology, Hefei 230031, People's Republic of China
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7
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Sriram S, Natiq H, Rajagopal K, Krejcar O, Krejcar O. Dynamics of a two-layer neuronal network with asymmetry in coupling. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:2908-2919. [PMID: 36899564 DOI: 10.3934/mbe.2023137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Investigating the effect of changes in neuronal connectivity on the brain's behavior is of interest in neuroscience studies. Complex network theory is one of the most capable tools to study the effects of these changes on collective brain behavior. By using complex networks, the neural structure, function, and dynamics can be analyzed. In this context, various frameworks can be used to mimic neural networks, among which multi-layer networks are a proper one. Compared to single-layer models, multi-layer networks can provide a more realistic model of the brain due to their high complexity and dimensionality. This paper examines the effect of changes in asymmetry coupling on the behaviors of a multi-layer neuronal network. To this aim, a two-layer network is considered as a minimum model of left and right cerebral hemispheres communicated with the corpus callosum. The chaotic model of Hindmarsh-Rose is taken as the dynamics of the nodes. Only two neurons of each layer connect two layers of the network. In this model, it is assumed that the layers have different coupling strengths, so the effect of each coupling change on network behavior can be analyzed. As a result, the projection of the nodes is plotted for several coupling strengths to investigate how the asymmetry coupling influences the network behaviors. It is observed that although no coexisting attractor is present in the Hindmarsh-Rose model, an asymmetry in couplings causes the emergence of different attractors. The bifurcation diagrams of one node of each layer are presented to show the variation of the dynamics due to coupling changes. For further analysis, the network synchronization is investigated by computing intra-layer and inter-layer errors. Calculating these errors shows that the network can be synchronized only for large enough symmetric coupling.
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Affiliation(s)
- Sridevi Sriram
- Centre for Computational Biology, Chennai Institute of Technology, Chennai 600069, India
| | - Hayder Natiq
- Department of Computer Technology Engineering, College of Information Technology, Imam Ja'afar Al-Sadiq University, Baghdad 10001, Iraq
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Ondrej Krejcar
- Center for Basic and Applied Research, Faculty of Informatics and Management, University of Hradec Kralove, Hradec Kralove, Czechia
- Institute of Technology and Business in Ceske Budejovice, Ceske Budejovice, Czechia
- Department of Biomedical Engineering and Measurement, Faculty of Mechanical Engineering Technical University of Kosice, Slovakia
| | - Ondrej Krejcar
- Center for Basic and Applied Research, Faculty of Informatics and Management, University of Hradec Kralove, Hradec Kralove, Czechia
- School of Engineering, Monash University, Selangor, Malaysia
- College of Engineering and Science, Victoria University, Melbourne, Australia
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8
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Li Q, Larosz KC, Han D, Ji P, Kurths J. Basins of attraction of chimera states on networks. Front Physiol 2022; 13:959431. [PMID: 36160849 PMCID: PMC9493443 DOI: 10.3389/fphys.2022.959431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 08/02/2022] [Indexed: 11/13/2022] Open
Abstract
Networks of identical coupled oscillators display a remarkable spatiotemporal pattern, the chimera state, where coherent oscillations coexist with incoherent ones. In this paper we show quantitatively in terms of basin stability that stable and breathing chimera states in the original two coupled networks typically have very small basins of attraction. In fact, the original system is dominated by periodic and quasi-periodic chimera states, in strong contrast to the model after reduction, which can not be uncovered by the Ott-Antonsen ansatz. Moreover, we demonstrate that the curve of the basin stability behaves bimodally after the system being subjected to even large perturbations. Finally, we investigate the emergence of chimera states in brain network, through inducing perturbations by stimulating brain regions. The emerged chimera states are quantified by Kuramoto order parameter and chimera index, and results show a weak and negative correlation between these two metrics.
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Affiliation(s)
- Qiang Li
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
- Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai, China
- MOE Frontiers Center for Brain Science, Fudan University, Shanghai, China
| | - Kelly C. Larosz
- University Center UNIFATEB, Telêmaco Borba, Brazil
- Graduate Program in Chemical Engineering Federal Technological University of Paraná, Ponta Grossa, Brazil
- Physics Institute, University of São Paulo, Oscillation Control Group, São Paulo, Brazil
| | - Dingding Han
- School of Information Science and Technology, Fudan University, Shanghai, China
- *Correspondence: Dingding Han, ; Peng Ji,
| | - Peng Ji
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China
- Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai, China
- MOE Frontiers Center for Brain Science, Fudan University, Shanghai, China
- *Correspondence: Dingding Han, ; Peng Ji,
| | - Jürgen Kurths
- Research Institute of Intelligent Complex Systems, Fudan University, Shanghai, China
- Potsdam Institute for Climate Impact Research, Potsdam, Germany
- Humboldt University, Berlin, Germany
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9
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Li X, Lei Y, Ghosh D. Taming non-stationary chimera states in locally coupled oscillators. CHAOS (WOODBURY, N.Y.) 2022; 32:093152. [PMID: 36182401 DOI: 10.1063/5.0118034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Accepted: 09/01/2022] [Indexed: 06/16/2023]
Abstract
The imperfect traveling chimera (ITC) state is a novel non-stationary chimera pattern in which the incoherent domain of oscillators spreads into the coherent domain. We investigate the ITC state in locally coupled pendulum oscillators with heterogeneous driving forces. We introduce the heterogeneous phase value in the driving forces by two different ways, namely, the random phase from uniform distribution and random phase directions with identical amplitude. We discover two transition mechanisms from ITC to coherent state through traveling chimera-like state by taking the two different phase heterogeneity. The transition phenomena are investigated using cylindrical and polar coordinate phase spaces. In the numerical study, we propose a quantitative measurement named "spatiotemporal consistency" strength for distinguishing the ITC from the traveling one. Our research facilitates the exploration of potential applications of heterogeneous interactions in neuroscience.
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Affiliation(s)
- Xueqi Li
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Youming Lei
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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10
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Meng Y, Lai YC, Grebogi C. The fundamental benefits of multiplexity in ecological networks. J R Soc Interface 2022; 19:20220438. [PMID: 36167085 PMCID: PMC9514891 DOI: 10.1098/rsif.2022.0438] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Accepted: 09/01/2022] [Indexed: 11/12/2022] Open
Abstract
A tipping point presents perhaps the single most significant threat to an ecological system as it can lead to abrupt species extinction on a massive scale. Climate changes leading to the species decay parameter drifts can drive various ecological systems towards a tipping point. We investigate the tipping-point dynamics in multi-layer ecological networks supported by mutualism. We unveil a natural mechanism by which the occurrence of tipping points can be delayed by multiplexity that broadly describes the diversity of the species abundances, the complexity of the interspecific relationships, and the topology of linkages in ecological networks. For a double-layer system of pollinators and plants, coupling between the network layers occurs when there is dispersal of pollinator species. Multiplexity emerges as the dispersing species establish their presence in the destination layer and have a simultaneous presence in both. We demonstrate that the new mutualistic links induced by the dispersing species with the residence species have fundamental benefits to the well-being of the ecosystem in delaying the tipping point and facilitating species recovery. Articulating and implementing control mechanisms to induce multiplexity can thus help sustain certain types of ecosystems that are in danger of extinction as the result of environmental changes.
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Affiliation(s)
- Yu Meng
- Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King’s College, University of Aberdeen, AB24 3UE, UK
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
- Center for Systems Biology Dresden, Pfotenhauerstraße 108, Dresden 01307, Germany
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA
- Department of Physics, Arizona State University, Tempe, AZ 85287, USA
| | - Celso Grebogi
- Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King’s College, University of Aberdeen, AB24 3UE, UK
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11
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Shen Q, Liu Z. Remote firing propagation in the neural network of C. elegans. Phys Rev E 2021; 103:052414. [PMID: 34134291 DOI: 10.1103/physreve.103.052414] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2021] [Accepted: 05/10/2021] [Indexed: 11/07/2022]
Abstract
Understanding the mechanisms of firing propagation in brain networks has been a long-standing problem in the fields of nonlinear dynamics and network science. In general, it is believed that a specific firing in a brain network may be gradually propagated from a source node to its neighbors and then to the neighbors' neighbors and so on. Here, we explore firing propagation in the neural network of Caenorhabditis elegans and surprisingly find an abnormal phenomenon, i.e., remote firing propagation between two distant and indirectly connected nodes with the intermediate nodes being inactivated. This finding is robust to source nodes but depends on the topology of network such as the unidirectional couplings and heterogeneity of network. Further, a brief theoretical analysis is provided to explain its mechanism and a principle for remote firing propagation is figured out. This finding provides insights for us to understand how those cognitive subnetworks emerge in a brain network.
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Affiliation(s)
- Qiwei Shen
- School of Physics and Electronic Science, East China Normal University, Shanghai 200062, People's Republic of China
| | - Zonghua Liu
- School of Physics and Electronic Science, East China Normal University, Shanghai 200062, People's Republic of China
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12
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Wang Z, Liu Z. Effect of remote signal propagation in an empirical brain network. CHAOS (WOODBURY, N.Y.) 2021; 31:063126. [PMID: 34241283 DOI: 10.1063/5.0054296] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Accepted: 05/28/2021] [Indexed: 06/13/2023]
Abstract
Increasing evidence has shown that brain functions are seriously influenced by the heterogeneous structure of a brain network, but little attention has been paid to the aspect of signal propagation. We here study how a signal is propagated from a source node to other nodes on an empirical brain network by a model of bistable oscillators. We find that the unique structure of the brain network favors signal propagation in contrast to other heterogeneous networks and homogeneous random networks. Surprisingly, we find an effect of remote propagation where a signal is not successfully propagated to the neighbors of the source node but to its neighbors' neighbors. To reveal its underlying mechanism, we simplify the heterogeneous brain network into a heterogeneous chain model and find that the accumulation of weak signals from multiple channels makes a strong input signal to the next node, resulting in remote propagation. Furthermore, a theoretical analysis is presented to explain these findings.
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Affiliation(s)
- Zhenhua Wang
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, People's Republic of China
| | - Zonghua Liu
- School of Physics and Electronic Science, East China Normal University, Shanghai 200241, People's Republic of China
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13
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Xiong K, Yan Z, Xie Y, Liu Z. Regulating heat conduction of complex networks by distributed nodes masses. Sci Rep 2021; 11:5501. [PMID: 33750886 PMCID: PMC7943792 DOI: 10.1038/s41598-021-85011-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Accepted: 02/15/2021] [Indexed: 01/31/2023] Open
Abstract
Developing efficient strategy to regulate heat conduction is a challenging problem, with potential implication in the field of thermal materials. We here focus on a potential thermal material, i.e. complex networks of nanowires and nanotubes, and propose a model where the mass of each node is assigned proportional to its degree with [Formula: see text], to investigate how distributed nodes masses can impact the heat flow in a network. We find that the heat conduction of complex network can be either increased or decreased, depending on the controlling parameter [Formula: see text]. Especially, there is an optimal heat conduction at [Formula: see text] and it is independent of network topologies. Moreover, we find that the temperature distribution within a complex network is also strongly influenced by the controlling parameter [Formula: see text]. A brief theoretical analysis is provided to explain these results. These findings may open up appealing applications in the cases of demanding either increasing or decreasing heat conduction, and our approach of regulating heat conduction by distributed nodes masses may be also valuable to the challenge of controlling waste heat dissipation in highly integrated and miniaturized modern devices.
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Affiliation(s)
- Kezhao Xiong
- College of Science, Xi'an University of Science and Technology, Xi'an, 710054, People's Republic of China.
- Department of Physics, Fudan University, Shanghai, 200433, People's Republic of China.
| | - Zhengxin Yan
- College of Science, Xi'an University of Science and Technology, Xi'an, 710054, People's Republic of China
| | - You Xie
- College of Science, Xi'an University of Science and Technology, Xi'an, 710054, People's Republic of China
| | - Zonghua Liu
- School of Physics and Electronic Science, East China Normal University, Shanghai, 200062, People's Republic of China.
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14
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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: 12] [Impact Index Per Article: 3.0] [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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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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