Robustness of chimera states for coupled FitzHugh-Nagumo oscillators

TL;DR

This paper investigates the robustness of chimera states in networks of FitzHugh-Nagumo oscillators, showing they persist under various inhomogeneities and topological modifications, with changes in stability and structure.

Contribution

It demonstrates the robustness of chimera states in inhomogeneous and irregular networks, and explores how different topologies affect their properties and stability.

Findings

Chimera states are robust to inhomogeneities in oscillator properties.

Modifications in coupling topology alter the stability regions of chimera states.

Hierarchical connectivity induces nested coherent and incoherent regions.

Abstract

Chimera states are complex spatio-temporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics. This counterintuitive phenomenon was first observed in systems of identical oscillators with symmetric coupling topology. Can one overcome these limitations? To address this question, we discuss the robustness of chimera states in networks of FitzHugh-Nagumo oscillators. Considering networks of inhomogeneous elements with regular coupling topology, and networks of identical elements with irregular coupling topologies, we demonstrate that chimera states are robust with respect to these perturbations, and analyze their properties as the inhomogeneities increase. We find that modifications of coupling topologies cause qualitative changes of chimera states: additional random links induce a shift of the stability regions in the system parameter plane, gaps in the connectivity matrix result in a change of the multiplicity of incoherent regions of the chimera state, and hierarchical geometry in the connectivity matrix induces nested coherent and incoherent regions.