Multi-cluster chimeras in phase oscillators with repulsive nonlocal coupling

TL;DR

This paper investigates multi-cluster chimera states in phase oscillators with nonlocal repulsive coupling, revealing phase relationships and stability conditions through numerical and analytical methods.

Contribution

It introduces the formation and stability analysis of multi-cluster chimeras with nonlocal repulsive coupling, contrasting them with attractive coupling cases.

Findings

Multi-cluster chimeras exhibit clusters in antiphase or splay configurations.

Stable parameter regions for these chimeras are identified.

Numerical results are validated by Ott-Antonsen analysis.

Abstract

Local repulsive coupling tend to a desynchronize ensembles of globally coupled oscillators, but when the repulsive coupling is nonlocal, multi-cluster chimeras can result. In this case, several groups of synchronized oscillators (the so-called clusters) are formed, and these coexist with a set of desynchronized oscillators. For phase oscillators on a ring with nonlocal piecewise linear repulsive coupling that also involves a phase lag, we find that in the multi-cluster chimera state the synchronized clusters are either antiphase or in splay with respect to each other, namely the n consecutive synchronized clusters differ in phase by 2{\pi}/n. This is in contrast to multi-cluster chimeras that are formed with nonlocal attractive coupling. The synchronized solutions are studied numerically as well as analytically and by analysing their stability, we identify the parameter regions where these can be observed. Our numerical results are validated by dimensional reduction using the Ott-Antonsen analysis.