Chaotic Behavior of a Mechanical Pendulum with Random Parametric Excitations : Evaluating Determinism

Abstract

This paper studies a random vibration of chaotic mechanical system with stochastic excitation. To dates, studies of mechanical chaotic vibrations have mainly focused on their deterministic properties. However, stochastic properties of mechanical system are sometimes unavoidable especially in practical situations. We have already shown that stabilities and scaling properties of experimental chaotic behavior are well modeled by stochastic models rather than deterministic models. We also have demonstrated that errors in deterministic modeling are getting larger in non-chaotic region. These results seem to imply that stability reduces determinism of stochastic behavior. In this paper, we evaluate determinism of the target stochastic behavior as a function of a bifurcation parameter. For this purpose, we use the Wayland's test and chaotic synchronizations. The two methods give distinct results. Dependency of stability of target stochastic behavior on accuracy of their deterministic and stochastic descriptions is clearly evaluated by the chaotic synchronizations.