The full text of this article is unavailable through your IP address: 3.144.89.197
Contents Online
Communications in Mathematical Sciences
Volume 21 (2023)
Number 7
Emergence of phase-locked states for a deterministic and stochastic Winfree model with inertia
Pages: 1875 – 1894
DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n7.a6
Authors
Abstract
We study the emergence of phase-locking for Winfree oscillators under the effect of inertia. It is known that in a large coupling regime, oscillators governed by the deterministic second-order Winfree model with inertia converge to a unique equilibrium. In contrast, in this paper we show the asymptotic emergence of non-trivial synchronization in a suitably small coupling regime. Moreover, we study the effect of a new stochastically perturbed Winfree system with multiplicative noise and obtain lower estimates in probability for the pathwise emergence of such a synchronizing pattern, provided the noise is sufficiently small. We also provide numerical simulations which hint at the possibility of more general and stronger analytical results.
Keywords
Winfree model, inertia, multiplicative noise, synchronization
2010 Mathematics Subject Classification
34F05, 70F40, 92B25
Received 22 July 2022
Received revised 22 December 2022
Accepted 20 January 2023
Published 9 October 2023