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The dynamics near a border-collision bifurcation are approximated to leadingorder by a continuous, piecewise-linear map. The purpose of this paper is toconsider the higher-order terms that are neglected when forming thisapproximation. For two-dimensional maps we establish conditions under which achaotic attractor created in a border-collision bifurcation persists for anopen interval of parameters beyond the bifurcation. We apply the results to aprototypical power converter model to prove the model exhibits robust chaos.

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