Bifurcations in nonlinear discontinuous systems

Abstract

In this paper a theory for bifurcations of discontinuous systems is presented. First, Filippov’s theory for the definition of solutions of discontinuous systems is surveyed. Furthermore, jumps in fundamental solution matrices are discussed. The paper treats discontinuous bi-furcations of fixed points and periodic solutions. It is shown how jumps in the fundamental solution matrix lead to jumps of the Floquet multipliers of periodic solutions. The Floquet multipliers can jump through the unit circle causing discontinuous bifurcations. Numerical examples are treated which show various discontinuous bifurcations. Also infinitely unstable solutions are addressed.