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

M Di Bernardo, PS Kowalczyk, A Nordmark

Research output: Contribution to journalArticle (Academic Journal)peer-review

245 Citations (Scopus)

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.
Translated title of the contributionBifurcations in Dynamical Systems with Sliding: Derivation of Normal Form Mappings
Original languageEnglish
Pages (from-to)175 - 205
Number of pages31
JournalPhysica D: Nonlinear Phenomena
Volume170
DOIs
Publication statusPublished - Sept 2002

Bibliographical note

Publisher: Elsevier BV

Research Groups and Themes

  • Engineering Mathematics Research Group

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