Bifurcation phenomena in non-smooth dynamical systems

R.I. Leine, D.H. Campen, van

Research output: Contribution to journalArticleAcademicpeer-review

111 Citations (Scopus)

Abstract

The aim of the paper is to give an overview of bifurcation phenomena which are typical for non-smooth dynamical systems. A small number of well-chosen examples of various kinds of non-smooth systems will be presented, followed by a discussion of the bifurcation phenomena in hand and a brief introduction to the mathematical tools which have been developed to study these phenomena. The bifurcations of equilibria in two planar non-smooth continuous systems are analysed by using a generalised Jacobian matrix. A mechanical example of a non-autonomous Filippov system, belonging to the class of differential inclusions, is studied and shows a number of remarkable discontinuous bifurcations of periodic solutions. A generalisation of the Floquet theory is introduced which explains bifurcation phenomena in differential inclusions. Lastly, the dynamics of the Woodpecker Toy is analysed with a one-dimensional Poincaré map method. The dynamics is greatly influenced by simultaneous impacts which cause discontinuous bifurcations.
Original languageEnglish
Pages (from-to)595-616
JournalEuropean Journal of Mechanics. A, Solids
Volume25
Issue number4
DOIs
Publication statusPublished - 2006

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