Chimera states in two-dimensional networks of locally coupled oscillators

Abstract

Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart - Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. The existence of chimera states is confirmed by instantaneous angular frequency, order parameter and strength of incoherence.

Accepted for publication in Phys. Rev. E (2018)

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• Chimera states in small disordered optomechanical arrays
• Traveling chimera patterns in two-dimensional neuronal network
• Spiral wave chimeras in reaction-diffusion systems: phenomenon, mechanism and transitions
• Two-dimensional optical chimera states in an array of coupled waveguide resonators
• Amplitude mediated spiral chimera pattern in a nonlinear reaction-diffusion system
• Spiral wave chimera-like transient dynamics in three-dimensional grid of diffusive ecological systems
• Synchronization patterns in LIF Neural Networks: Merging Nonlocal and Diagonal Connectivity
• Dynamic effects of electric field in hybrid coupling thermosensitive neuronal network
• Spiral wave chimeras in populations of oscillators coupled to a slowly varying diffusive environment
• Chimera and anticoordination states in learning dynamics