Inclusion of higher-order terms in the border-collision normal form: Persistence of chaos and applications to power converters
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Date
2024-06
Open Access Location
Authors
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Publisher
Elsevier BV
Rights
(c) 2024 The Author/s
CC BY 4.0
CC BY 4.0
Abstract
The dynamics near a border-collision bifurcation are approximated to leading order by a continuous, piecewise-linear map. The purpose of this paper is to consider the higher-order terms that are neglected when forming this approximation. For two-dimensional maps we establish conditions under which a chaotic attractor created in a border-collision bifurcation persists for an open interval of parameters beyond the bifurcation. We apply the results to a prototypical power converter model to prove the model exhibits robust chaos.
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Keywords
Robust chaos, Piecewise-smooth systems, Hybrid systems, Border-collision bifurcation
Citation
Simpson DJW, Glendinning PA. (2024). Inclusion of higher-order terms in the border-collision normal form: Persistence of chaos and applications to power converters. Physica D: Nonlinear Phenomena. 462.