Twisted chimera states and multicore spiral chimera states on a two-dimensional torus

Xie, Jian‐bo; Knobloch, Edgar; Kao, Hsuan-Yun

doi:10.1103/physreve.92.042921

Cited by 64 publications

(61 citation statements)

References 19 publications

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“…Recently, works involving two [36,37] and three-dimensional [38] oscillator arrays have revealed new types of chimera states, depending on the coupling function. These studies have mainly focused on phase oscillators.…”

Section: Introductionmentioning

confidence: 99%

Chimera patterns in two-dimensional networks of coupled neurons

et al. 2017

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We discuss synchronization patterns in networks of FitzHugh-Nagumo and Leaky Integrate-andFire oscillators coupled in a two-dimensional toroidal geometry. Common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes including spots, rings, stripes, and grids, observed in both models, as well as additional patterns found mainly in the FitzHughNagumo system. Both systems exhibit multistability: For the same parameter values, different initial conditions give rise to different dynamical states. Transitions occur between various patterns when the parameters (coupling range, coupling strength, refractory period, and coupling phase) are varied. Many patterns observe in the two models follow similar rules. For example the diameter of the rings grows linearly with the coupling radius.

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Section: Introductionmentioning

confidence: 99%

Chimera patterns in two-dimensional networks of coupled neurons

et al. 2017

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“…The analysis of the competition between strategy associations is generally based on models with random sequential imitation type evolutionary rule that may even be applied simultaneously for several systems [348] when the models become similar to stochastic cellular automata [349,350]. The spatial rock-paper-scissor game with a synchronized stochastic logit update [351] has demonstrated the appearance of chimera states which have been intensively studied in the literature of coupled spatial oscillators [352,353,354,355,356]. For the repeated two-player rock-paper-scissors game the synchronized logit rule at low noises results in cyclic choices [e.g.…”

Section: Effects Of Rock-paper-scissors Gamementioning

confidence: 99%

Evolutionary potential games on lattices

2016

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Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide scale of biological objects, human individuals, or even their associations. In these systems the interactions are characterized by matrices that can be decomposed into elementary matrices (games) and classified into four types. The concept of decomposition helps the identification of potential games and also the evaluation of the potential that plays a crucial role in the determination of the preferred Nash equilibrium, and defines the Boltzmann distribution towards which these systems evolve for suitable types of dynamical rules. This survey draws parallel between the potential games and the kinetic Ising type models which are investigated for a wide scale of connectivity structures. We discuss briefly the applicability of the tools and concepts of statistical physics and thermodynamics. Additionally the general features of ordering phenomena, phase transitions and slow relaxations are outlined and applied to evolutionary games. The discussion extends to games with three or more strategies. Finally we discuss what happens when the system is weakly driven out of the "equilibrium state" by adding non-potential components representing games of cyclic dominance.

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“…Oscillators of numerous varieties have also been coupled via long-range interactions on lattices (and more general network structures) [25,26]. In fact, until recently, they were often assumed to be a fundamental ingredient for the formation of so-called 'chimera states' [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear excitations in magnetic lattices with long-range interactions

et al. 2019

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We study-experimentally, theoretically, and numerically-nonlinear excitations in lattices of magnets with long-range interactions. We examine breather solutions, which are spatially localized and periodic in time, in a chain with algebraically-decaying interactions. It was established two decades ago (Flach 1998 Phys. Rev. E 58 R4116) that lattices with long-range interactions can have breather solutions in which the spatial decay of the tails has a crossover from exponential to algebraic decay. In this article, we revisit this problem in the setting of a chain of repelling magnets with a mass defect and verify, both numerically and experimentally, the existence of breathers with such a crossover.

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Twisted chimera states and multicore spiral chimera states on a two-dimensional torus

Cited by 64 publications

References 19 publications

Chimera patterns in two-dimensional networks of coupled neurons

Chimera patterns in two-dimensional networks of coupled neurons

Evolutionary potential games on lattices

Nonlinear excitations in magnetic lattices with long-range interactions

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