Hyperbolicity impedes emergence of chimera states in networks of nonlocally coupled chaotic oscillators

TL;DR

This paper investigates how hyperbolicity affects the formation of chimera states in networks of chaotic oscillators, showing that hyperbolic systems hinder their emergence while nonhyperbolic systems support them.

Contribution

It provides analytical and numerical evidence that hyperbolicity impedes chimera states, a novel insight into the dynamics of coupled chaotic systems.

Findings

Chimera states only occur in nonhyperbolic chaotic networks.

Hyperbolic systems do not exhibit chimera states.

Analytical and numerical results support the hypothesis.

Abstract

We analyze nonlocally coupled networks of identical chaotic oscillators with either time-discrete or time-continuous dynamics (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of nonhyperbolic chaotic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by analytical results and numerical simulations for hyperbolic and nonhyperbolic cases.