Characteristic distribution of finite-time Lyapunov exponents for chimera states

TL;DR

This paper demonstrates that the probability density functions of finite-time Lyapunov exponents have a unique shape for chimera states, enabling their detection even when oscillator phases are inaccessible.

Contribution

It introduces a novel method to identify chimera states through characteristic Lyapunov exponent distributions, useful for systems with unmeasurable phases.

Findings

Characteristic Lyapunov exponent distributions serve as signatures of chimera states

Distribution shapes can be obtained indirectly via embedding techniques

Method enables detection of chimera states in systems with unmeasurable phases

Abstract

It is shown that probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a characteristic shape. Such distributions could be used as a signature of chimera states, particularly in systems for which the phases of all the oscillators cannot be measured directly. In such cases, the characteristic distribution may be obtained indirectly, via embedding techniques, thus making it possible to detect chimera states in systems where they could otherwise exist, unnoticed.