Dynamics of large oscillator populations with random interactions
Adaptation and Self-Organizing Systems
2024-07-19 v1 Disordered Systems and Neural Networks
Abstract
We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence of the phases and the couplings, we derive reduced averaged equations with effective non-random coupling terms. As a particular example, we study interactions that have the same shape but possess random coupling strengths and random phase shifts. While randomness in coupling strengths just renormalizes the interaction, a distribution of the phase shifts in coupling reshapes the coupling function.
Cite
@article{arxiv.2404.06193,
title = {Dynamics of large oscillator populations with random interactions},
author = {Arkady Pikovsky and Lev A. Smirnov},
journal= {arXiv preprint arXiv:2404.06193},
year = {2024}
}