Discontinuous bifurcations of periodic solutions. (Q1410097)

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.