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

2021/11/24 by David J. W. Simpson, Simpson, David J. W., Paul Glendinning +2
Computer Science · Mathematics · Physics and Astronomy · #37G35 #39A28 #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #math.DS #msc:37G35 #msc:39A28

paper · pdf · doi:10.48550/arxiv.2111.12222

arxiv created 2021/11/24 · openalex publication_date 2021/11/24 · arxiv updated 2021/11/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

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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