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

TL;DR

This paper models globally coupled two-state stochastic oscillators with a state-dependent refractory period, revealing a transition from quiescent to oscillatory behavior as coupling strength increases.

Contribution

It introduces a novel model where the refractory period depends on the global state, leading to new insights into the synchronization transition in stochastic oscillators.

Findings

Weak coupling results in a stationary state.

Increasing coupling induces a saddle node bifurcation.

Beyond critical coupling, oscillations emerge.

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.