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Mathematics > Dynamical Systems

arXiv:2205.13844 (math)
[Submitted on 27 May 2022]

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

Authors:Myeongju Kang, Marco Rehmeier
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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.
Comments: 10 figures
Subjects: Dynamical Systems (math.DS); Classical Analysis and ODEs (math.CA); Probability (math.PR)
Cite as: arXiv:2205.13844 [math.DS]
  (or arXiv:2205.13844v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.2205.13844

Submission history

From: Marco Rehmeier [view email]
[v1] Fri, 27 May 2022 09:13:08 UTC (573 KB)
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