Border-collision bifurcations in a driven time-delay system

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Border-collision bifurcations in a driven time-delay system

Ryan, Pierce; Keane, Andrew; Amann, Andreas
Date: 2020-02-07
Copyright: © 2020, the Authors. Published under license by AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the authors and AIP Publishing. This article appeared as: Ryan, P., Keane, A. and Amann, A. (2020) 'Border-collision bifurcations in a driven time-delay system', Chaos, 30(2), 023121 (12pp), doi: 10.1063/1.5119982, and may be found at https://doi.org/10.1063/1.5119982
Full text restriction information: Access to this article is restricted until 12 months after publication by request of the publisher.
Restriction lift date: 2021-02-07
Citation: Ryan, P., Keane, A. and Amann, A. (2020) 'Border-collision bifurcations in a driven time-delay system', Chaos, 30(2), 023121 (12pp). doi: 10.1063/1.5119982
Published Version: 10.1063/1.5119982

Abstract:

We show that a simple piecewise-linear system with time delay and periodic forcing gives rise to a rich bifurcation structure of torus bifurcations and Arnold tongues, as well as multistability across a significant portion of the parameter space. The simplicity of our model enables us to study the dynamical features analytically. Specifically, these features are explained in terms of border-collision bifurcations of an associated Poincaré map. Given that time delay and periodic forcing are common ingredients in mathematical models, this analysis provides widely applicable insight.

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