EMERGENCE OF PHASE-LOCKED STATES FOR THE WINFREE MODEL IN A LARGE COUPLING REGIME

Abstract

We study the large-time behavior of the globally coupled Winfree model in a large coupling regime. The Winfree model is the first mathematical model for the synchronization phenomenon in an ensemble of weakly coupled limit-cycle oscillators. For the dynamic formation of phase-locked states, we provide a sufficient framework in terms of geometric conditions on the coupling functions and coupling strength. We show that in the proposed framework, the emergent phase-locked state is the unique equilibrium state and it is asymptotically stable in an l1-norm; further, we investigate its configurational structure. We also provide several numerical simulations, and compare them with our analytical results.