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arXiv · 2002.03948

Border-collision bifurcations in a driven time-delay system

Pierce Ryan·Andrew Keane·Andreas Amann
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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 Poincar\'e map. Given that time delay and periodic forcing are common ingredients in mathematical models, this analysis provides widely applicable insight.

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Pierce Ryan, Andrew Keane, Andreas Amann. 2020-02-10. Border-collision bifurcations in a driven time-delay system. https://doi.org/10.1063/1.5119982

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