Analysis on the chaotic motion of a stochastic nonlinear dynamic system

Abstract

Based on the stochastic nonlinear dynamic theory, the stochastic Melnikov method and rate of phase space flux theory, we studied the chaotic motion of a forced vibration system with cubic nonlinear item and square resistance item in this article. It becomes especially difficult to calculate the simple zero of the Melnikov function because of the presence of stochastic item. By introducing the rate of phase space flux function theory, using the relation between the rate of phase space flux function and the stochastic Melnikov function, we only need to calculate the zero of the rate of phase space flux function. This article not only obtained the condition for the chaotic motion, but also greatly simplified the calculation. This method has some practical meaning for the relevant researches in engineering and economic fields.

Keywords:

• bounded noise
• chaotic
• stochastic Melnikov function
• rate of phase space flux function

2000 AMS Subject Classifications :

• 34L30
• 37D45
• 93E03

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 60641006).