Bifurcations in Nonlinear Discontinuous Systems

This paper treats bifurcations of periodic solutions indiscontinuous systems of the Filippov type. Furthermore, bifurcations offixed points in non-smooth continuous systems are addressed. Filippov'stheory for the definition of solutions of discontinuous systems issurveyed and jumps in fundamental solution matrices are discussed. It isshown how jumps in the fundamental solution matrix lead to jumps of theFloquet multipliers of periodic solutions. The Floquet multipliers canjump through the unit circle causing discontinuous bifurcations.Numerical examples are treated which show various discontinuousbifurcations. Also infinitely unstable periodic solutions are addressed.