Bifurcation of dynamical Systems with sliding: derivations of normal-form mappings

Authors: di Bernardo, M., Kowalczyk, P., Nordmark, A.
Document Type: Article
Pubstate: Published
Journal: Physica D
Volume: 170   175-205
Year: 2002


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.