Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays

TL;DR

This paper investigates the existence and stability of synchronous solutions in a continuum of non-locally coupled phase oscillators with propagation delays, providing a stability diagram, heuristic conditions, and analytic relations.

Contribution

It offers a comprehensive stability analysis, including a stability diagram and analytic expressions, for non-locally coupled oscillators with delays, advancing understanding of their synchronization behavior.

Findings

A stability diagram in parameter space is developed.

A heuristic synchronization condition is proposed.

An analytic relation for the marginal stability curve is derived.

Abstract

We study the existence and stability of synchronous solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. We present a comprehensive stability diagram in the parameter space of the system. From the numerical results a heuristic synchronization condition is suggested, and an analytic relation for the marginal stability curve is obtained. We also provide an expression in the form of a scaling relation that closely follows the marginal stability curve over the complete range of the non-locality parameter.