Chimera states in nonlocally coupled bicomponent phase oscillators: From synchronous to asynchronous chimeras

TL;DR

This paper demonstrates the existence of chimera states in nonlocally coupled bicomponent phase oscillators, showing a transition from synchronous to asynchronous states as the frequency difference increases, revealing new dynamical behaviors.

Contribution

It introduces the concept of chimera states in bicomponent oscillators with varying natural frequencies and characterizes the transition from synchronous to asynchronous chimeras.

Findings

Chimera states exist regardless of the magnitude of frequency difference.

Synchronous chimeras occur at small frequency differences.

Asynchronous chimeras occur at large frequency differences.

Abstract

Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units, prevail in a variety of systems. Here, we consider a population of nonlocally coupled bicomponent phase oscillators in which oscillators with natural frequency $\omega_0$ (positive oscillators) and $-\omega_0$ (negative oscillators) are randomly distributed along a ring. We show the existence of chimera states no matter how large $\omega_0$ is and the states manifest themselves in the form that oscillators with positive/negative frequency support their own chimera states. There are two types of chimera states, synchronous chimera states at small $\omega_0$ in which coherent positive and negative oscillators share a same mean phase velocity and asynchronous chimera states at large $\omega_0$ in which coherent positive and negative oscillators have different mean phase velocities. Increasing $\omega_0$ induces a desynchronization transition between synchronous chimera states and asynchronous chimera states.