1
|
Fateev I, Polezhaev A. Synchronization transitions in a system of superdiffusively coupled neurons: Interplay of chimeras, solitary states, and phase waves. CHAOS (WOODBURY, N.Y.) 2024; 34:093131. [PMID: 39312726 DOI: 10.1063/5.0226751] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2024] [Accepted: 09/02/2024] [Indexed: 09/25/2024]
Abstract
In this paper, a network of interacting neurons based on a two-component system of reaction-superdiffusion equations with fractional Laplace operator responsible for the coupling configuration and nonlinear functions of the Hindmarsh-Rose model is considered. The process of synchronization transition in the space of the fractional Laplace operator exponents is studied. This parametric space contains information about both the local interaction strength and the asymptotics of the long-range couplings for both components of the system under consideration. It is shown that in addition to the homogeneous transition, there are regions of inhomogeneous synchronization transition in the space of the fractional Laplace operator exponents. Weak changes of the corresponding exponents in inhomogeneous zones are associated with the significant restructuring of the dynamic modes in the system. The parametric regions of chimera states, solitary states, phase waves, as well as dynamical modes combining them, are determined. The development of filamentary structures associated with the manifestation of different partial synchronization modes has been detected. In view of the demonstrated link between changes in network topology and internal dynamics, the data obtained in this study may be useful for neuroscience tasks. The approaches used in this study can be applied to a wide range of natural science disciplines.
Collapse
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
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
3
|
Kongni SJ, Nguefoue V, Njougouo T, Louodop P, Ferreira FF, Tchitnga R, Cerdeira HA. Phase transitions on a multiplex of swarmalators. Phys Rev E 2023; 108:034303. [PMID: 37849080 DOI: 10.1103/physreve.108.034303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Accepted: 08/01/2023] [Indexed: 10/19/2023]
Abstract
Dynamics of bidirectionally coupled swarmalators subject to attractive and repulsive couplings is analyzed. The probability of two elements in different layers being connected strongly depends on a defined vision range r_{c} which appears to lead both layers in different patterns while varying its values. Particularly, the interlayer static sync π has been found and its stability is proven. First-order transitions are observed when the repulsive coupling strength σ_{r} is very small for a fixed r_{c} and, moreover, in the absence of the repulsive coupling, they also appear for sufficiently large values of r_{c}. For σ_{r}=0 and for sufficiently small values of r_{c}, both layers achieve a second-order transition in a surprising two steps that are characterized by the drop of the energy of the internal phases while increasing the value of the interlayer attractive coupling σ_{a} and later a smooth jump, up to high energy value where synchronization is achieved. During these transitions, the internal phases present rotating waves with counterclockwise and later clockwise directions until synchronization, as σ_{a} increases. These results are supported by simulations and animations added as supplemental materials.
Collapse
Affiliation(s)
- Steve J Kongni
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon and MoCLiS Research Group, Dschang, Cameroon
| | - Venceslas Nguefoue
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon and MoCLiS Research Group, Dschang, Cameroon
| | - Thierry Njougouo
- Faculty of Computer Science and naXys Institute, University of Namur, 5000 Namur, Belgium; Namur Institute for Complex Systems (naXys), University of Namur, Belgium; Department of Electrical and Electronic Engineering, Faculty of Engineering and Technology (FET), University of Buea, P. O. Box 63, Buea, Cameroon; and MoCLiS Research Group, Dschang, Cameroon
| | - Patrick Louodop
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon; ICTP South American Institute for Fundamental Research, São Paulo State University (UNESP), Instituto de Física Teórica, 01140-070 São Paulo, Brazil; and MoCLiS Research Group, Dschang, Cameroon
| | - Fernando Fagundes Ferreira
- Center for Interdisciplinary Research on Complex Systems, University of Sao Paulo, São Paulo 03828-000, Brazil; and Department of Physics-FFCLRP, University of São Paulo, Ribeirão Preto, SP 14040-901, Brazil
| | - Robert Tchitnga
- Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P. O. Box 67 Dschang, Cameroon
| | - Hilda A Cerdeira
- São Paulo State University (UNESP), Instituto de Física Teórica, 01140-070 São Paulo, Brazil and Epistemic, Gomez & Gomez Ltda. ME, 05305-031 São Paulo, Brazil
| |
Collapse
|
4
|
Boaretto BRR, Budzinski RC, Rossi KL, Manchein C, Prado TL, Feudel U, Lopes SR. Bistability in the synchronization of identical neurons. Phys Rev E 2021; 104:024204. [PMID: 34525513 DOI: 10.1103/physreve.104.024204] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2021] [Accepted: 07/19/2021] [Indexed: 11/07/2022]
Abstract
We investigate the role of bistability in the synchronization of a network of identical bursting neurons coupled through an generic electrical mean-field scheme. These neurons can exhibit distinct multistable states and, in particular, bistable behavior is observed when their sodium conductance is varied. With this, we consider three different initialization compositions: (i) the whole network is in the same periodic state; (ii) half of the network periodic, half chaotic; (iii) half periodic, and half in a different periodic state. We show that (i) and (ii) reach phase synchronization (PS) for all coupling strengths, while for (iii) small coupling regimes do not induce PS, and instead, there is a coexistence of different frequencies. For stronger coupling, case (iii) synchronizes, but after (i) and (ii). Since PS requires all neurons being in the same state (same frequencies), these different behaviors are governed by transitions between the states. We find that, during these transitions, (ii) and (iii) have transient chimera states and that (iii) has breathing chimeras. By studying the stability of each state, we explain the observed transitions. Therefore, bistability of neurons can play a major role in the synchronization of generic networks, with the simple initialization of the system being capable of drastically changing its asymptotic space.
Collapse
Affiliation(s)
- B R R Boaretto
- Department of Physics, Universidade Federal do Paraná, 81531-980, Curitiba, PR, Brazil
| | - R C Budzinski
- Department of Physics, Universidade Federal do Paraná, 81531-980, Curitiba, PR, Brazil
| | - K L Rossi
- Department of Physics, Universidade Federal do Paraná, 81531-980, Curitiba, PR, Brazil
| | - C Manchein
- Department of Physics, Universidade do Estado de Santa Catarina, 89219-710 Joinville, SC, Brazil
| | - T L Prado
- Department of Physics, Universidade Federal do Paraná, 81531-980, Curitiba, PR, Brazil
| | - U Feudel
- Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University Oldenburg, 26111 Oldenburg, Germany
| | - S R Lopes
- Department of Physics, Universidade Federal do Paraná, 81531-980, Curitiba, PR, Brazil
| |
Collapse
|
5
|
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.
Collapse
Affiliation(s)
| | - Zonghua Liu
- School of Physics and Electronic Science, East China Normal University, Shanghai, China
| |
Collapse
|
6
|
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]
|
7
|
Andrzejak RG, Ruzzene G, Schöll E, Omelchenko I. Two populations of coupled quadratic maps exhibit a plentitude of symmetric and symmetry broken dynamics. CHAOS (WOODBURY, N.Y.) 2020; 30:033125. [PMID: 32237754 DOI: 10.1063/5.0002272] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 02/28/2020] [Indexed: 06/11/2023]
Abstract
We numerically study a network of two identical populations of identical real-valued quadratic maps. Upon variation of the coupling strengths within and across populations, the network exhibits a rich variety of distinct dynamics. The maps in individual populations can be synchronized or desynchronized. Their temporal evolution can be periodic or aperiodic. Furthermore, one can find blends of synchronized with desynchronized states and periodic with aperiodic motions. We show symmetric patterns for which both populations have the same type of dynamics as well as chimera states of a broken symmetry. The network can furthermore show multistability by settling to distinct dynamics for different realizations of random initial conditions or by switching intermittently between distinct dynamics for the same realization. We conclude that our system of two populations of a particularly simple map is the most simple system that can show this highly diverse and complex behavior, which includes but is not limited to chimera states. As an outlook to future studies, we explore the stability of two populations of quadratic maps with a complex-valued control parameter. We show that bounded and diverging dynamics are separated by fractal boundaries in the complex plane of this control parameter.
Collapse
Affiliation(s)
- Ralph G Andrzejak
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
| | - Giulia Ruzzene
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, Carrer Roc Boronat 138, 08018 Barcelona, Catalonia, Spain
| | - Eckehard Schöll
- 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
| |
Collapse
|
8
|
Kaminker V, Wackerbauer R. Alternating activity patterns and a chimeralike state in a network of globally coupled excitable Morris-Lecar neurons. CHAOS (WOODBURY, N.Y.) 2019; 29:053121. [PMID: 31154794 DOI: 10.1063/1.5093483] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2019] [Accepted: 04/30/2019] [Indexed: 06/09/2023]
Abstract
Spatiotemporal chaos collapses to either a rest state or a propagating pulse in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Adding global varying synaptic coupling to the ring network reveals complex transient behavior. Spatiotemporal chaos collapses into a transient pulse that reinitiates spatiotemporal chaos to allow sequential pattern switching until a collapse to the rest state. A domain of irregular neuron activity coexists with a domain of inactive neurons forming a transient chimeralike state. Transient spatial localization of the chimeralike state is observed for stronger synapses.
Collapse
Affiliation(s)
- Vitaliy Kaminker
- Department of Physics, University of Alaska, Fairbanks, Alaska 99775-5920, USA
| | - Renate Wackerbauer
- Department of Physics, University of Alaska, Fairbanks, Alaska 99775-5920, USA
| |
Collapse
|
9
|
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.
Collapse
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
| |
Collapse
|
10
|
Majhi S, Bera BK, Ghosh D, Perc M. Chimera states in neuronal networks: A review. Phys Life Rev 2018; 28:100-121. [PMID: 30236492 DOI: 10.1016/j.plrev.2018.09.003] [Citation(s) in RCA: 133] [Impact Index Per Article: 22.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2018] [Accepted: 09/10/2018] [Indexed: 11/19/2022]
Abstract
Neuronal networks, similar to many other complex systems, self-organize into fascinating emergent states that are not only visually compelling, but also vital for the proper functioning of the brain. Synchronous spatiotemporal patterns, for example, play an important role in neuronal communication and plasticity, and in various cognitive processes. Recent research has shown that the coexistence of coherent and incoherent states, known as chimera states or simply chimeras, is particularly important and characteristic for neuronal systems. Chimeras have also been linked to the Parkinson's disease, epileptic seizures, and even to schizophrenia. The emergence of this unique collective behavior is due to diverse factors that characterize neuronal dynamics and the functioning of the brain in general, including neural bumps and unihemispheric slow-wave sleep in some aquatic mammals. Since their discovery, chimera states have attracted ample attention of researchers that work at the interface of physics and life sciences. We here review contemporary research dedicated to chimeras in neuronal networks, focusing on the relevance of different synaptic connections, and on the effects of different network structures and coupling setups. We also cover the emergence of different types of chimera states, we highlight their relevance in other related physical and biological systems, and we outline promising research directions for the future, including possibilities for experimental verification.
Collapse
Affiliation(s)
- Soumen Majhi
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Bidesh K Bera
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India.
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia; School of Electronic and Information Engineering, Beihang University, Beijing 100191, China.
| |
Collapse
|
11
|
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.
Collapse
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
| |
Collapse
|
12
|
Chouzouris T, Omelchenko I, Zakharova A, Hlinka J, Jiruska P, Schöll E. Chimera states in brain networks: Empirical neural vs. modular fractal connectivity. CHAOS (WOODBURY, N.Y.) 2018; 28:045112. [PMID: 31906648 DOI: 10.1063/1.5009812] [Citation(s) in RCA: 46] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and incoherent domains and can be observed in networks of coupled oscillators. The interplay of synchrony and asynchrony in complex brain networks is an important aspect in studies of both the brain function and disease. We analyse the collective dynamics of FitzHugh-Nagumo neurons in complex networks motivated by its potential application to epileptology and epilepsy surgery. We compare two topologies: an empirical structural neural connectivity derived from diffusion-weighted magnetic resonance imaging and a mathematically constructed network with modular fractal connectivity. We analyse the properties of chimeras and partially synchronized states and obtain regions of their stability in the parameter planes. Furthermore, we qualitatively simulate the dynamics of epileptic seizures and study the influence of the removal of nodes on the network synchronizability, which can be useful for applications to epileptic surgery.
Collapse
Affiliation(s)
- Teresa Chouzouris
- 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
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Jaroslav Hlinka
- Institute of Computer Science, Czech Academy of Sciences, Pod Vodarenskou vezi 2, 18207 Prague, Czech Republic
| | - Premysl Jiruska
- Institute of Physiology, Czech Academy of Sciences, Videnska 1083, 14220 Prague, Czech Republic
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| |
Collapse
|
13
|
Ratas I, Pyragas K. Symmetry breaking in two interacting populations of quadratic integrate-and-fire neurons. Phys Rev E 2018; 96:042212. [PMID: 29347512 DOI: 10.1103/physreve.96.042212] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2017] [Indexed: 11/07/2022]
Abstract
We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both inherently spiking and excitable neurons. The coupling within and between the populations is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rates and the mean membrane potentials in both populations. The reduced equations are exact in the infinite-size limit. The bifurcation analysis of the equations reveals a rich variety of nonsymmetric patterns, including a splay state, antiphase periodic oscillations, chimera-like states, and chaotic oscillations as well as bistabilities between various states. The validity of the reduced equations is confirmed by direct numerical simulations of the finite-size networks.
Collapse
Affiliation(s)
- Irmantas Ratas
- Center for Physical Sciences and Technology, LT-10257 Vilnius, Lithuania
| | - Kestutis Pyragas
- Center for Physical Sciences and Technology, LT-10257 Vilnius, Lithuania
| |
Collapse
|
14
|
Bauer L, Bassett J, Hövel P, Kyrychko YN, Blyuss KB. Chimera states in multi-strain epidemic models with temporary immunity. CHAOS (WOODBURY, N.Y.) 2017; 27:114317. [PMID: 29195311 DOI: 10.1063/1.5008386] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We investigate a time-delayed epidemic model for multi-strain diseases with temporary immunity. In the absence of cross-immunity between strains, dynamics of each individual strain exhibit emergence and annihilation of limit cycles due to a Hopf bifurcation of the endemic equilibrium, and a saddle-node bifurcation of limit cycles depending on the time delay associated with duration of temporary immunity. Effects of all-to-all and non-local coupling topologies are systematically investigated by means of numerical simulations, and they suggest that cross-immunity is able to induce a diverse range of complex dynamical behaviors and synchronization patterns, including discrete traveling waves, solitary states, and amplitude chimeras. Interestingly, chimera states are observed for narrower cross-immunity kernels, which can have profound implications for understanding the dynamics of multi-strain diseases.
Collapse
Affiliation(s)
- Larissa Bauer
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Jason Bassett
- 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
| | - Yuliya N Kyrychko
- Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom
| | - Konstantin B Blyuss
- Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom
| |
Collapse
|
15
|
Bera BK, Ghosh D, Parmananda P, Osipov GV, Dana SK. Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback control. CHAOS (WOODBURY, N.Y.) 2017; 27:073108. [PMID: 28764407 DOI: 10.1063/1.4993459] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report the emergence of coexisting synchronous and asynchronous subpopulations of oscillators in one dimensional arrays of identical oscillators by applying a self-feedback control. When a self-feedback is applied to a subpopulation of the array, similar to chimera states, it splits into two/more sub-subpopulations coexisting in coherent and incoherent states for a range of self-feedback strength. By tuning the coupling between the nearest neighbors and the amount of self-feedback in the perturbed subpopulation, the size of the coherent and the incoherent sub-subpopulations in the array can be controlled, although the exact size of them is unpredictable. We present numerical evidence using the Landau-Stuart system and the Kuramoto-Sakaguchi phase model.
Collapse
Affiliation(s)
- Bidesh K Bera
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Punit Parmananda
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - G V Osipov
- Department of Control Theory, Nizhni Novgorod State University, Gagarin Avenue 23, 606950 Nizhni Novgorod, Russia
| | - Syamal K Dana
- Department of Mathematics, Jadavpur University, Kolkata 700032, India
| |
Collapse
|