Emergence of phase-locked states for a deterministic and stochastic Winfree model with inertia

Autor:	Kang, Myeongju, Rehmeier, Marco
Rok vydání:	2022
Předmět:	Mathematics - Dynamical Systems Mathematics - Classical Analysis and ODEs Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	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. Comment: 10 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.13844 Zobrazit plný text záznamu View this record from Arxiv