Stable chimeras of non-locally coupled Kuramoto-Sakaguchi oscillators in a finite array

Abstract

We consider chimera states of coupled identical phase oscillators where some oscillators are phase synchronized while others are desynchronized. It is known that chimera states of non-locally coupled Kuramoto--Sakaguchi oscillators in arrays of finite size are chaotic transients when the phase lag parameter $\alpha \in (0, \pi/2)$; after a transient time, all the oscillators are phase synchronized, with the transient time increasing exponentially with the number of oscillators. In this work, we consider a small array of six non-locally coupled oscillators with the phase lag parameter $\alpha \in (\pi/2, \pi)$ in which the complete phase synchronization of the oscillators is unstable. Under these circumstances, we observe a chimera state spontaneously formed by the partition of oscillators into two independently synchronizable clusters of both stable and unstable synchronous states. We provide numerical evidence supporting that the instantaneous frequencies of the oscillators of the chimera state are periodic functions of time with a common period, and as a result, the chimera state is stable but not long-lived transient. We also measure the basin stability of the chimera state and show that it can be observed for random initial conditions when $\alpha$ is slightly larger than $\pi/2$.