Browsing by Author "Glendinning PA"

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    Inclusion of higher-order terms in the border-collision normal form: Persistence of chaos and applications to power converters
    (Elsevier BV, 2024-06) Simpson DJW; Glendinning PA
    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.