On synchronization of coupled Hopf-Kuramoto oscillators with phase delays

Abstract

This paper presents new methods and results on synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs). On balanced graphs, any positive coupling gain is proven to induce almost global asymptotic synchronization, and a threshold value for truly global exponential synchronization is also computed. Furthermore, a hierarchical connection between coupled Hopf oscillators and Kuramoto oscillators is identified. Finally, a new result on the synchronization of Kuramoto oscillators with arbitrary time-varying heterogeneous frequencies and delays is derived.

Additional Information

© 2010 IEEE. Date Added to IEEE Xplore: 22 February 2011. This work was supported in part by the Air Force Office of Scientific Research (AFOSR).

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