Emergent dynamics of Winfree oscillators on locally coupled networks

[Published in Journal of Differential Equations, 260 (2016), no. 5, 4203 - 4236.]

[Preprint version]

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

(To see the Winfree model)

We study the emergent dynamics of the Winfree model on a locally coupled static network. For the emergence of complete or partial oscillator deaths (COD, POD), we provided sufficient frameworks in terms of connection topology, coupling strength, and coupling functions. Moreover, our results for COD and POD covered generic initial data in the case of special sensitivity and influence functions S(\theta)=-\sin\theta and I(\theta) = 1 + \cos\theta, in large coupling regimes. We also provided three qualitative estimates; in particular, we considered the existence of an attractor with positive measures, exponential \ell_1-contractivity, and the existence of an equilibrium inside the attractor of a large-coupling regime.