Border-collision bifurcations in a driven time-delay system

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Date
2020-02-07
Authors
Ryan, Pierce
Keane, Andrew
Amann, Andreas
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AIP Publishing
Published Version
10.1063/1.5119982
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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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Piecewise-linear system , Time delay , Periodic forcing , Torus bifurcations , Arnold tongues , Border-collision bifurcations , Poincaré map , ~Mathematical Sciences- Journal Articles~
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
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https://hdl.handle.net/10468/9951
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School of Mathematical Sciences
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© 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