Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators

TL;DR

This paper extends the phase oscillator model to nonlocal coupling, revealing coexistence of synchronized and desynchronized domains, and introduces a self-consistency theory validated by numerical simulations.

Contribution

It develops a theoretical framework for nonlocal coupling in phase oscillators, explaining the emergence of mixed coherence-incoherence patterns.

Findings

Coexistence of synchronized and desynchronized domains observed.

Self-consistency equation accurately predicts pattern formation.

Numerical solutions match simulation results closely.

Abstract

The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into two domains, one composed of mutually synchronized oscillators with unique frequency and the other composed of desynchronized oscillators with distributed frequencies. We apply a theory similar to the one which successfully explained the onset of collective synchronization in globally coupled phase oscillators with frequency distribution. A space-dependent order parameter is thus introduced, and an exact functional self-consistency equation is derived for this quantity. Its numerical solution is confirmed to reproduce the simulation results accurately.