Large-scale spatio-temporal patterns in a ring of non-locally coupled oscillators with a repulsive coupling

TL;DR

This study investigates large-scale spatio-temporal patterns in a ring of non-locally coupled oscillators with repulsive coupling, revealing phase transitions and the reappearance of complex states as the phase delay parameter varies.

Contribution

It numerically analyzes the effects of phase delay on patterns in non-locally coupled oscillators, identifying phase transitions and the reemergence of multi-chimera states.

Findings

Multi-chimera state disappears beyond a critical phase delay.

Transition behavior resembles directed percolation but with different criticality.

Multi-chimera states reappear at higher phase delays, leading to five collective phases.

Abstract

Non-locally coupled oscillators with a phase lag exhibit various non-trivial spatio-temporal patterns such as the chimera states and the multi-twisted states. We numerically study large-scale spatio-temporal patterns in a ring of oscillators with a repulsive coupling with a phase delay parameter $\alpha$. We find that the multi-chimera state disappears when $\alpha$ exceeds a critical value. Analyzing the density of incoherent regions, we show that the transition is analogous to that of directed percolation with two absorbing states, but their critical behaviors are different. The multi-chimera state reappears when $\alpha$ is further increased, exhibiting non-trivial spatio-temporal patterns with a plateau in the density of incoherent regions. A transition from the multi-chimera to multi-twisted states follows at a larger value of $\alpha$, resulting in five collective phases in total.