Defect states as a precursor of the chimera states in a ring of non-locally coupled oscillators

TL;DR

This paper explores how defect states in a ring of non-locally coupled oscillators act as precursors to chimera states, revealing how intermediate defect dynamics relate to the transition from synchronization to chimera patterns.

Contribution

It identifies defect states as dynamical precursors to chimera states and analyzes their properties and dependence on phase delay in non-locally coupled oscillators.

Findings

Defect states increase with phase delay and peak at crossover point.

Traveling speed, number, and width of defects grow with phase delay.

Total spatial extent of defects remains consistent across system sizes.

Abstract

We investigate the transition from synchronized to chimera states in a ring of non-locally coupled phase oscillators. Our focus is on the intermediate defect states, where solitary waves in the phase gradient profile travel at a constant speed. These traveling defects serve as a dynamical precursor for the nucleation of chimera clusters. The fraction of samples exhibiting defect states increases with the phase delay $\alpha$ and peaks at $\alpha_{c}$, where the system crosses over to asynchronous states filled with chimera clusters. While the traveling speed, number, and width of these defects increase with $\alpha$, the total spatial extent of the defects remains robust against the system size $N$. These results shed new light on the emergence of chimera states in frustrated coupled oscillators.