Chimera states in a neuronal network under the action of an electric field

Simo, Gaël R.; Njougouo, Thierry; Aristides, Raul P.; Louodop, Patrick; Tchitnga, Robert; Cerdeira, Hilda A.

doi:10.1103/physreve.103.062304

Cited by 19 publications

(6 citation statements)

References 49 publications

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“…Regarding the data of table 1, contrarily to what is usual in the literature, we give all the possible algebraic expressions (second column) of the corresponding diagram (first column), which are obviously fixed-point subspaces of conjugate isotropies. Doing so, we link the data of tables 1 and 2: expressions (1) to (3) of ♯1 in table 1 appear in table 2 ♯6 but not in ♯2; similarly, the expressions (19) to (22) of ♯6 in table 1 appear in ♯6 but only (21) appear in ♯6 of table 2, and so on.…”

Section: Coupled Network Of Van Der Pol Identical Oscillatorsmentioning

confidence: 99%

“…One particular motivation to carry out with this procedure relies on the approach of a many works to study 'chimera' states of a vector field (section 5). We cite [1,[18][19][20][21] for example, and [24] for a timely overview on the subject. A chimera state is a peculiar partial synchronisation patterns in networks, defined as a spatio-temporal pattern in which a system of identical oscillators is split into coexisting regions of coherent (phase and frequency locked) and incoherent (drifting) oscillation [1].…”

Section: Introductionmentioning

confidence: 99%

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The realisation of admissible graphs for coupled vector fields

Amorim,

Manoel

2023

Nonlinearity

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In a coupled network cells can interact in several ways. There is a vast literature from the last 20 years that investigates this interacting dynamics under a graph theory formalism, namely as a graph endowed with an input-equivalence relation on the set of vertices that enables a characterisation of the admissible vector fields that rules the network dynamics. The present work goes in the direction of answering an inverse problem: for n ⩾ 2 , any mapping on R n can be realised as an admissible vector field for some graph with the number of vertices depending on (but not necessarily equal to) n. Given a mapping, we present a procedure to construct all non-equivalent admissible graphs, up to the appropriate equivalence relation. We also give an upper bound for the number of such graphs. As a consequence, invariant subspaces under the vector field can be investigated as the locus of synchrony states supported by an admissible graph, in the sense that a suitable graph can be chosen to realise couplings with more (or less) synchrony than another graph admissible to the same vector field. The approach provides in particular a systematic investigation of occurrence of chimera states in a network of van der Pol identical oscillators.

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Section: Coupled Network Of Van Der Pol Identical Oscillatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The realisation of admissible graphs for coupled vector fields

Amorim,

Manoel

2023

Nonlinearity

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“…Recently, chimera or chimeralike states in neuronal networks have attracted great attentions, and rich interesting phenomena are reported [29][30][31][32]. For example, Wang et al found the chimeras in an adaptive neuronal network with burst-timing-dependent plasticity [29].…”

Section: Introductionmentioning

confidence: 99%

Alternate attractor chimeralike states on rings of chaotic Lorenz-type oscillators

Zhang,

Chen,

Liu

et al. 2024

New J. Phys.

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An interesting alternate attractor chimeralike state can self-organize to emerge on rings of chaotic Lorenz-type oscillators. The local dynamics of any two neighboring oscillators can spontaneously change from the chaotic butterfly-like attractors to the two symmetric and converse ones, which forms alternate attractors on the ring. This is distinctly different from the traditional chimera states with unique local attractor. An effective driven-oscillator approach is proposed to reveal the mechanism in forming this new oscillation mode and predict the critical coupling strengths for the emergence of the new oscillation mode. The existence of a pair of converse focus solutions with respect to the external drive is found to be the key factor responsible for the alternate attractor chimeralike state. The linear feedback control scheme is introduced to control the suppression and reproduction of alternate attractor chimeralike state. These findings may shed light on a new perspective of the studies and applications of chimera dynamics in complex systems.

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“…More interestingly, Simo et al [34] revealed traveling chimera patterns in a 2-D HR neural network. Simo et al [35] studied a set of 3-D HR neurons in the presence of an electric field. As a result, traveling chimera states and multicluster oscillating breathers were discovered in the absence of the field.…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics of a heterogeneous network of Hindmarsh-Rose neurons

et al. 2023

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This contribution is devoted to the study of the collective behavior of two HR neurons followed by a network of HR neurons. The collective behavior of the two coupled neuron was obtained from the connection between the traditional 3D HR and a memristive 2D HR neuron via a gap junction. The dynamical properties of this rst topology revealed that it is dissipative therefore can support complex phenomena. From numerical simulations, it is found that the coupled neurons display a variety of behaviors just by varying the control parameter. Amongst these behaviors found, we have periodic bursting or spiking, quasi-periodic bursting or spiking, and chaotic bursting or spiking. Non-synchronized motion is observed when the electrical coupling strength is weak. However, synchronized cluster states are observed when the coupling strength is increased. Also varied of cross ring networks made of combination of N = 100 these different HR neurons in the network are also investigated. It is discovered that the spatiotemporal patterns are affected by the network topology. The cluster states are represented in the non- homogenous network's ring and star structures. The ring and ring-star structures contain single and double-well chimera states. Finally, in the PSIM simulation environment, a comparable electronic circuit for the two coupled heterogeneous neurons is designed and investigated. The results obtained from the designed analog circuit and the mathematical model of the two coupled neurons match perfectly.

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Chimera states in a neuronal network under the action of an electric field

Cited by 19 publications

References 49 publications

The realisation of admissible graphs for coupled vector fields

The realisation of admissible graphs for coupled vector fields

Alternate attractor chimeralike states on rings of chaotic Lorenz-type oscillators

Complex dynamics of a heterogeneous network of Hindmarsh-Rose neurons

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