Chimeras on a ring of oscillator populations

Abstract

Chimeras occur in networks of coupled oscillators and are characterized by coexisting groups of synchronous oscillators and asynchronous oscillators. We consider a network formed from N equal-sized populations at equally spaced points around a ring. We use the Ott/Antonsen ansatz to derive coupled ordinary differential equations governing the level of synchrony within each population and describe chimeras using a self-consistency argument. For N=2 and 3, our results are compared with previously known ones. We obtain new results for the cases of 4,5,…,12 populations and a numerically based conjecture resulting from the behavior of larger numbers of populations. We find macroscopic chaos when more than five populations are considered, but conjecture that this behavior vanishes as the number of populations is increased.