Coherence-incoherence patterns in a ring of non-locally coupled phase oscillators (Q2852518)

This paper considers the dynamics of a ring of identical phase oscillators, coupled non-locally through a sinusoidal function of their phase differences. The continuum limit is taken (number of oscillators tends to \(\infty\)), resulting in a non-local continuity equation. The Ott/Antonsen ansatz is used to reduce the dynamics to a non-local differential equation for a spatially-dependent complex order parameter. Much of the paper consists of a rigorous analysis of this equation, giving both existence and stability of a variety of different solutions, and their dependence on parameters. Among these solutions are ``chimera'' states, where regions of coherent oscillators alternate with regions of incoherent oscillators. The analysis enables a classification of these states, and suggests new patterns that may be observed.