# Emergence of phase-locked states for the Winfree model in a large coupling regime

[Published in Discrete and Continuous Dynamical Systems - Series A, 35 (2015), no. 8, 3417-3436.]

[Preprint version]

This is a joint work with Seung-Yeal Ha and Sang Woo Ryoo.

(To see the Winfree model)

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 $\ell_1$-norm; further, we investigate its configurational structure. We also provide several numerical simulations, and compare them with our analytical results.