Chaotic behaviors of nonlinear vibration system with stochastic excitation: (Probability distribution of local expansion rates)

Abstract

This paper reports on the study of chaotic behavior of nonlinear vibration systems with stochastic excitation. Previous studies examining mechanical chaotic vibrations have mainly focused on their deterministic properties even if the target system contains stochastic elements which are sometimes unavoidable in experimental situations. In view of this, this paper investigates random vibrations arising in nonlinear stochastic systems, which the authors call SCB (stochastic chaotic behavior). SCB has negative largest Liapunov exponents while it behaves similarly to deterministic chaos, exhibiting the expanding and folding process of chaos. This feature of SCB is in good agreement with that of a experimental chaotic behavior observed in our experiments and implies that the physical chaotic behavior may not have positive largest Liapunov exponents even though it behaves chaotically. These kinds of chaotic properties of SCB and experimental chaos can be characterized by the probability density function of local expansion rates.