Bifurcation Analysis of Stochastic Non-smooth Systems

Abstract

Non-smooth systems with stochastic parameters are important models e.g. for brake and cam follower systems. They show special bifurcation phenomena, such as grazing bifurcations. This contribution studies the influence of stochastic processes on bifurcations in non-smooth systems. As an example, the classical mass on a belt system is considered, where stick-slip vibrations occur. Measurements indicate that the friction coefficient which plays a large role in the system behavior is not deterministic but can be described as a friction characteristic with added white noise. Therefore, a stochastic process is introduced into the non-smooth model and its influence on the bifurcation behavior is studied. It is shown that the stochastic process may alter the bifurcation behavior of the deterministic system.