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n:m Phase-locking of weakly coupled oscillators

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Two weakly coupled oscillators are studied and the existence of n:m phase-locked solutions is shown. With the use of a slow time scale, the problem is reduced to a two-dimensional system on an invariant attracting torus. This system is further reduced to a one-dimensional dynamical system. Fixed points of this system correspond to n:m phase-locked solutions. The method is applied to a forced oscillator, linearly coupled λ-ω systems, and a pair of integrate and fire neuron models.

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Ermentrout, G.B. n:m Phase-locking of weakly coupled oscillators. J. Math. Biology 12, 327–342 (1981).

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