Bifurcations of dynamical systems with sliding : derivation of normal-form mappings

M di Bernardo, PS Kowalczyk, A Nordmark

Research output: Working paperWorking paper and Preprints

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Abstract

This paper is concerned with the analysis of so-called sliding bifurcations in n-dimensional piecewise-smooth dynamical systems with discontinuous vector field. These novel bifurcations occur when the system trajectory interacts with regions on the discontinuity set where sliding is possible. The derivation of appropriate normal form maps is detailed. It is shown that the leading order term in the map depends on the particular bifurcation scenario considered. This is in turn related to the possible bifurcation scenarios exhibited by a periodic orbit undergoing one of the sliding bifurcations discussed in the paper. A third-order relay system serves as a numerical example.
Original languageEnglish
Publication statusPublished - 2001

Bibliographical note

Additional information: Preprint of a paper later published by Elsevier Science (2002), Physica D : Nonlinear Phenomena, 170(3-4), pp.175-205, ISSN 0167-2789

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