Bifurcation phenomena in non-smooth dynamical systems

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 introduc...

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Veröffentlicht in:European journal of mechanics, A, Solids A, Solids, 2006-07, Vol.25 (4), p.595-616
Hauptverfasser: Leine, R.I., van Campen, D.H.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0997-7538
1873-7285
DOI:10.1016/j.euromechsol.2006.04.004