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

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.

5 pages, 6 figures

References in corpus (4)

• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Directed percolation criticality in turbulent liquid crystals
• Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators
• Mechanism for intensity induced chimera states in globally coupled oscillators