Chaotic Weak Chimeras and their Persistence in Coupled Populations of Phase Oscillators

TL;DR

This paper investigates the existence and persistence of chaotic weak chimera states in coupled phase oscillator populations, demonstrating that such states can persist even with vanishing inter-population coupling and positive Lyapunov exponents.

Contribution

It provides new theoretical results on the persistence of chaotic weak chimeras in coupled oscillator networks, including cases with minimal coupling.

Findings

Chaotic weak chimeras can exist with vanishing coupling.

Positive Lyapunov exponents can persist over a range of coupling strengths.

Numerical evidence supports the robustness of these states.

Abstract

Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoherent oscillations. The recently-introduced notion of a weak chimera gives a rigorously testable characterization of chimera states for finite-dimensional phase oscillator networks. In this paper we give some persistence results for dynamically invariant sets under perturbations and apply them to coupled populations of phase oscillators with generalized coupling. In contrast to the weak chimeras with nonpositive maximal Lyapunov exponents constructed so far, we show that weak chimeras that are chaotic can exist in the limit of vanishing coupling between coupled populations of phase oscillators. We present numerical evidence that positive Lyapunov exponents can persist for a positive measure set of this inter-population coupling strength.