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

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 $α$ and peaks at $α_{c}$, where the system crosses over to asynchronous states filled with chimera clusters. While the traveling speed, number, and width of these defects increase with $α$, 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.

💡 Research Summary

The paper investigates how synchronized states give way to chimera states in a ring of non‑locally coupled phase oscillators, focusing on an intermediate “defect state”. The authors consider a one‑dimensional ring of N identical phase oscillators with sinusoidal coupling limited to a range R and a constant phase lag α (0 < α < ½). The dynamics are described by

 dϕₓ/dt = −(1/2R) ∑_{|x−y|_md≤R} sin