Slowly Coupled Oscillators: Phase Dynamics and Synchronization

SIAM Journal on Applied Mathematics (2003) 63:1935-1953

Eugene M. Izhikevich and Frank C. Hoppensteadt

Abstract. In this paper we extend the results of Frankel and Kiemel [SIAM J. Appl. Math, 53 (1993), pp.~1436--1446] to a network of slowly coupled oscillators. First, we use Malkinís theorem to derive a canonical phase model that describes synchronization properties of a slowly coupled network. Then, we illustrate the result using slowly coupled oscillators (1) near Andronov-Hopf bifurcations, (2) near saddle-node on invariant circle bifurcations, and (3) relaxation oscillations. We compare and contrast synchronization properties of slowly and weakly coupled oscillators.

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