Discontinuous bifurcations of periodic solutions. (English) Zbl 1046.34016

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.


34A36 Discontinuous ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
Full Text: DOI


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