Detecting chimeras by eigenvalue decomposition of the bivariate local order parameter

Parastesh, Fatemeh; Azarnoush, Hamed; Jafari, Sajad; Perc, Matjaž

doi:10.1209/0295-5075/130/28003

Cited by 5 publications

(2 citation statements)

References 56 publications

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“…This phenomenon was later termed the chimera state [17]. Recently, chimera states have been explored in different systems and using different types of couplings [18][19][20][21][22][23][24][25]. Chimera states are analogously to the cerebral behaviors of certain aquatic mammals and migratory birds, which during their movements half part of their brains asleep while the rest are awake [26,27].…”

Section: Introductionmentioning

confidence: 99%

Traveling chimera patterns in two-dimensional neuronal network

Simo,

Louodop,

Ghosh

et al. 2021

Preprint

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We study the emergence of the traveling chimera state in a two-dimensional network of Hindmarsh-Rose burst neurons with the mutual presence of local and non-local couplings. We show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera, ie the presence in the network under study, of patterns of coherent elements interspersed by other incoherent elements in movement and alternately changing their position over time. The confirmation of the states of coherence is done by introducing the parameter of instantaneous local order parameter in two dimensions. We extend our analysis through mathematical tools such as the Hamilton energy function to determine the direction of propagation of patterns in two dimensions.

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Section: Introductionmentioning

confidence: 99%

Traveling chimera patterns in two-dimensional neuronal network

Simo,

Louodop,

Ghosh

et al. 2021

Preprint

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“…Variation of the number of neighbors and the coupling coefficient can change the network behavior and arrange the oscillators in the synchronous, asynchronous, or chimera state. The statistical measure strength of incoherence (SI) is used to quantify the spatial coherence-incoherence pattern and chimera state [41]. For calculating this measure, the network's oscillators are divided into M bins of equal length n = N/M where n is an even number [42].…”

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confidence: 99%

Chimera states in coupled memristive chaotic systems: Effects of control parameters

Ramamoorthy¹,

Shahriari²,

Natiq³

et al. 2022

EPL

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The study of the collective behavior of oscillators has grabbed great attention in recent years. Among all dynamical systems, multi-stable systems have received particular attention. This paper considers a ring network of non-locally coupled VB5 chaotic systems exhibiting multistability with linear coupling. The collective patterns of the oscillators are investigated by taking various internal parameters of memristors as the bifurcation parameter. The network’s state is characterized by computing the strength of incoherence. Moreover, the variations of the coupling strength and the number of neighbors in connections are considered to check out the coupling effects. The synchronous, chimera, and asynchronous states are visible in the network under different parameters. It is observed that as the dynamics of the oscillators become more complex, the behavior of the network transits to more asynchrony. The results also show that the network represents the chimera state both in monostable and multistable modes. In monostable mode, the oscillators of the synchronized and asynchronized groups belong to one attractor. In contrast, in the multistable mode, each group oscillates in one of the existing attractors.

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