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 |
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| container_title | European journal of mechanics, A, Solids |
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| creator | Leine, R.I. van Campen, D.H. |
| description | 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. |
| doi_str_mv | 10.1016/j.euromechsol.2006.04.004 |
| format | Article |
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| subjects | Bifurcation Discontinuity Exact sciences and technology Friction Fundamental areas of phenomenology (including applications) Impact Measure differential inclusions Physics Solid mechanics |
| title | Bifurcation phenomena in non-smooth dynamical systems |
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