Large-scale spatiotemporal patterns in a ring of nonlocally coupled oscillators with a repulsive coupling.

Abstract

Nonlocally coupled oscillators with a phase lag exhibit various nontrivial spatiotemporal patterns such as the chimera states and the multitwisted states. We numerically study large-scale spatiotemporal patterns in a ring of oscillators with a repulsive coupling with a phase delay parameter α. We find that the multichimera state disappears when α exceeds a critical value. Analysis of the fraction of incoherent regions shows that the transition is analogous to that of directed percolation with two absorbing states but that their critical behaviors are different. The multichimera state reappears when α is further increased, exhibiting nontrivial spatiotemporal patterns with a plateau in the fraction of incoherent regions. A transition from the multichimera to multitwisted states follows at a larger value of α, resulting in five collective phases in total.