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

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.

6 pages, 7 figures