Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays
Adaptation and Self-Organizing Systems
2026-01-27 v2
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.
Keywords
Cite
@article{arxiv.1003.5079,
title = {Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays},
author = {Gautam C Sethia and Abhijit Sen and Fatihcan M. Atay},
journal= {arXiv preprint arXiv:1003.5079},
year = {2026}
}
Comments
accepted in Phys. Rev. E (2010)