Clustering in Globally Coupled Oscillators Near a Hopf Bifurcation: Theory and Experiments
Adaptation and Self-Organizing Systems
2014-09-17 v3 Disordered Systems and Neural Networks
Chemical Physics
Abstract
A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators.
Keywords
Cite
@article{arxiv.1401.4803,
title = {Clustering in Globally Coupled Oscillators Near a Hopf Bifurcation: Theory and Experiments},
author = {Hiroshi Kori and Yoshiki Kuramoto and Swati Jain and István Z. Kiss and John Hudson},
journal= {arXiv preprint arXiv:1401.4803},
year = {2014}
}
Comments
15 pages, 5 figures