Bifurcation phenomena in non-smooth dynamical systems

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

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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.
Originele taal-2Engels
Pagina's (van-tot)595-616
TijdschriftEuropean Journal of Mechanics. A, Solids
Volume25
Nummer van het tijdschrift4
DOI's
StatusGepubliceerd - 2006

Vingerafdruk

Bifurcation (mathematics)
dynamical systems
Dynamical systems
inclusions
Jacobian matrices
causes

Citeer dit

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Bifurcation phenomena in non-smooth dynamical systems. / Leine, R.I.; Campen, van, D.H.

In: European Journal of Mechanics. A, Solids, Vol. 25, Nr. 4, 2006, blz. 595-616.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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