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arXiv · 2111.12222

Inclusion of higher-order terms in the border-collision normal form: persistence of chaos and applications to power converters

David J. W. Simpson·Paul A. Glendinning
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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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David J. W. Simpson, Paul A. Glendinning. 2021-11-24. Inclusion of higher-order terms in the border-collision normal form: persistence of chaos and applications to power converters. https://arxiv.org/abs/2111.12222

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