title: 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.
authors.affiliation: Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Avenida San Carlos de Apoquindo 2200, Santiago, Chile.
authors.forename: Daniel
authors.initials: D
authors.lastname: Escaff
authors.forename: Upendra
authors.initials: U
authors.lastname: Harbola
authors.forename: Katja
authors.initials: K
authors.lastname: Lindenberg
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D009991:Oscillometry / Q000379:methods*; D013269:Stochastic Processes; D013997:Time Factors