Synchronization of globally coupled two-state stochastic oscillators with a state dependent refractory period

Abstract

We present a model of identical coupled two-state stochastic units each of which in isolation is governed by a fixed refractory period. The nonlinear coupling between units directly affects the refractory period, which now depends on the global state of the system and can therefore itself become time dependent. At weak coupling the array settles into a quiescent stationary state. Increasing coupling strength leads to a saddle node bifurcation, beyond which the quiescent state coexists with a stable limit cycle of nonlinear coherent oscillations. We explicitly determine the critical coupling constant for this transition.

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Cited by in corpus (5)

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• Tristable and multiple bistable activity in complex random binary networks of two-state units
• Damped oscillations of the probability of random events followed by absolute refractory period: exact analytical results