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

TL;DR

This paper investigates how higher-order terms affect chaos in border-collision bifurcations, demonstrating that chaos can persist beyond bifurcation points and applying findings to power converter models.

Contribution

It extends the border-collision normal form analysis by including higher-order terms, showing conditions for persistent chaos and applying results to power converter systems.

Findings

Chaotic attractors can persist over parameter ranges beyond bifurcation.

Higher-order terms influence the robustness of chaos in piecewise-linear maps.

Power converter models exhibit robust chaos under certain conditions.

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.