Bifurcations in nonlinear discontinuous systems

This paper treats bifurcations of periodic solutions in discontinuous syste ms of the Filippov type. Furthermore, bifurcations of fixed points in non-s mooth continuous systems are addressed. Filippov's theory for the definitio n of solutions of discontinuous systems is surveyed and jumps in fundamenta l solution matrices are discussed. It is shown how jumps in the fundamental solution matrix lead to jumps of the Floquet multipliers of periodic solut ions. The Floquet multipliers can jump through the unit circle causing disc ontinuous bifurcations. Numerical examples are treated which show various d iscontinuous bifurcations. Also infinitely unstable periodic solutions are addressed.