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The dynamics of a pair of coupled integrate-and-fire oscillators is studied. Previous work by Mirollo and Strogatz is extended here to include the more realistic case in which the oscillators have different natural frequencies. It is shown that, given sufficient coupling, oscillators with arbitrary natural frequencies can always be made to synchronize. Furthermore, the condition necessary and sufficient for synchronization is determined. It is also shown that for any given set of parameter values there is a single periodic trajectory toward which all initial conditions are attracted: neither chaos nor quasiperiodicity is possible.
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ADAM A. BRAILOVE (1992) studied this question.
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