The oscillating two-cluster chimera state in non-locally coupled phase oscillators

TL;DR

This paper demonstrates the existence of a dynamic two-cluster chimera state in non-locally coupled identical phase oscillators without delay, extending previous findings from delay-coupled systems and analyzing its behavior for finite systems.

Contribution

It reveals a novel oscillating two-cluster chimera state in non-delayed systems and provides theoretical analysis confirming its existence and dynamics.

Findings

Two-cluster chimera state exists in non-delayed systems.

Chimera state is not stationary for finite oscillators.

Theoretical analysis confirms the state and its dynamics.

Abstract

We investigate an array of identical phase oscillators non-locally coupled without time delay, and find that chimera state with two coherent clusters exists which is only reported in delay-coupled systems previously. Moreover, we find that the chimera state is not stationary for any finite number of oscillators. The existence of the two-cluster chimera state and its time-dependent behaviors for finite number of oscillators are confirmed by the theoretical analysis based on the self-consistency treatment and the Ott-Antonsen ansatz.