Stability of amplitude chimeras in oscillator networks

TL;DR

This paper investigates amplitude chimeras in ring networks of Stuart-Landau oscillators, revealing their saddle-state nature, analyzing their stability via Floquet exponents, and demonstrating their existence in minimal networks.

Contribution

It provides a detailed stability analysis of amplitude chimeras, showing they are saddle states with long transient lifetimes, and identifies the minimal network size exhibiting these states.

Findings

Amplitude chimeras are saddle states with unstable manifolds.

Floquet exponents depend on coupling strength and range.

Minimum network size for amplitude chimeras is N=12.

Abstract

We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of coherent and of incoherent oscillations. We calculate the Floquet exponents and the corresponding eigenvectors in dependence upon the coupling strength and range, and discuss the implications for the phase space structure. The existence of at least one positive real part of the Floquet exponents indicates an unstable manifold in phase space, which explains the nature of these states as long-living transients. Additionally, we find a Stuart-Landau network of minimum size $N=12$ exhibiting amplitude chimeras