Hopf Bifurcation in Two Groups of Delay-Coupled Kuramoto Oscillators
Abstract
Hopf bifurcation in two groups of Kuramoto's phase oscillators with delay-coupled interactions is investigated on the Ott–Antonsen's manifold. We find that the reduced delay differential system undergoes Hopf bifurcations when the coupling strength between two groups exceeds some critical values. With the increasing of time delay, stability switches are observed which leads to the synchrony switches for the Kuramoto system. The direction of Hopf bifurcation and the stability of bifurcating periodic solutions are investigated by deriving the normal forms on the center manifold. With respect to the Kuramoto system, simulations are performed to support our analytic results.
Supported by National Nature Science Foundation of China under grant nos. 11371112 and 11301117, by Heilongjiang Provincial Natural Science Foundation under grant no. QC2014C003 and by the Scientific Research Foundation of Harbin Institute of Technology at Weihai (HIT(WH) 201422).
