Integrable order parameter dynamics of globally coupled oscillators
Chaotic Dynamics
2016-06-28 v2 Exactly Solvable and Integrable Systems
Abstract
We study the nonlinear dynamics of globally coupled nonidentical oscillators in the framework of two order parameter (mean field and amplitude-frequency correlator) reduction. The main result of the paper is the exact solution of the corresponding nonlinear system on an attracting manifold. We present a complete classification of phase portraits and bifurcations, obtain explicit expressions for invariant manifolds (a limit cycle among them) and derive analytical solutions for arbitrary initial data and different regimes.
Cite
@article{arxiv.1606.02526,
title = {Integrable order parameter dynamics of globally coupled oscillators},
author = {G. M. Pritula and V. I. Prytula and O. V. Usatenko},
journal= {arXiv preprint arXiv:1606.02526},
year = {2016}
}