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

Discontinuous bifurcations of periodic solutions. (English) Zbl 1046.34016

Math. Comput. Modelling 36, No. 3, 259-273 (2002).
The authors discuss some aspects of bifurcations of periodic solutions in systems with a discontinuous vector field. Using the example \[ m\ddot x+C(\dot x) + K(x) = f_0\sin(\omega t), \] the authors demonstrate, under certain assumptions on the functions \(K(x)\) and \(C(\dot x)\), how the Floquet multipliers of a discontinuous system can jump when the system parameters are changed. Numerical examples show a discontinuous fold and symmetry-breaking bifurcations.
Reviewer: Anatoly Martynyuk (Kyïv)

Cited in 20 Documents

MSC:

34A36 Discontinuous ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations

Keywords:

discontinuous; bifurcation; stick-slip; dry friction
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\textit{R. I. Leine} and \textit{D. H. van Campen}, Math. Comput. Modelling 36, No. 3, 259--273 (2002; Zbl 1046.34016)
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References:

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