Synchronization of stochastic hybrid oscillators driven by a common switching environment
File(s)Chaos18b.pdf (937.8 KB)
Published version
Author(s)
Bressloff, PC
MacLaurin, J
Type
Journal Article
Abstract
Many systems in biology, physics, and chemistry can be modeled through ordinary differential equations (ODEs), which are piecewise smooth, but switch between different states according to a Markov jump process. In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we suppose that this limit ODE supports a stable limit cycle. We demonstrate that a set of such oscillators can synchronize when they are uncoupled, but they share the same switching Markov jump process. The latter is taken to represent the effect of a common randomly switching environment. We determine the leading order of the Lyapunov coefficient governing the rate of decay of the phase difference in the fast switching limit. The analysis bears some similarities to the classical analysis of synchronization of stochastic oscillators subject to common white noise. However, the discrete nature of the Markov jump process raises some difficulties: in fact, we find that the Lyapunov coefficient from the quasi-steady-state approximation differs from the Lyapunov coefficient one obtains from a second order perturbation expansion in the waiting time between jumps. Finally, we demonstrate synchronization numerically in the radial isochron clock model and show that the latter Lyapunov exponent is more accurate.
Date Issued
2018-12
Online Publication Date
2023-10-10T08:46:36Z
Date Acceptance
2018-11-30
ISSN
1054-1500
Publisher
AIP Publishing
Journal / Book Title
Chaos: An Interdisciplinary Journal of Nonlinear Science
Volume
28
Issue
12
Copyright Statement
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Paul C. Bressloff, James MacLaurin; Synchronization of stochastic hybrid oscillators driven by a common switching environment. Chaos 1 December 2018; 28 (12): 123123. and may be found at https://doi.org/10.1063/1.5054795
Identifier
http://dx.doi.org/10.1063/1.5054795
Publication Status
Published
Article Number
123123
Date Publish Online
2018-12-27