Physical Review E (1998), 58:905-908

Eugene M. Izhikevich

Systems Science Center, Box 7606,
Arizona State University,
Tempe, AZ 85287-7606.

Abstract. Studying weakly connected oscillators leads to phase models. It has been proven recently that weakly connected oscillators with delayed interactions do not lead to phase models with time delays even when the delay is of the same order of magnitude as the period of oscillation. This results in a fading interest to such models. We prove here that if the interaction delay between weakly connected oscillators is much longer than the period of oscillation, then the corresponding phase model does have an explicit time delay.

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