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

DOI10.1016/J.PHYSD.2024.134131arXiv2111.12222OpenAlexW3216187482MaRDI QIDQ6383806

P. Glendinning, D. J. W. Simpson

Publication date: 23 November 2021

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.

Full work available at URL: https://doi.org/10.1016/j.physd.2024.134131

Mathematics Subject Classification ID

Smooth dynamical systems: general theory (37Cxx) Dynamical systems with hyperbolic behavior (37Dxx) Local and nonlocal bifurcation theory for dynamical systems (37Gxx)

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