Multi-cluster chimeras in phase oscillators with repulsive nonlocal coupling

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 2π/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.