Chaotic motion of the dynamical system under both additive and multiplicative noise excitations  

作　　者：李秀春 徐伟 李瑞红 

机构地区：[1]Department of Applied Mathematics,Northwestern Polytechnical University

出　　处：《Chinese Physics B》2008年第2期557-568,共12页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant Nos 10472091 and 10332030)

摘　　要：With both additive and multiplicative noise excitations, the effect on the chaotic behaviour of the dynamical system is investigated in this paper. The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos. As an example, for the Duffing system, we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos, and by combining figures, we discuss the influences of the amplitude, intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately. Finally, numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincaré map.With both additive and multiplicative noise excitations, the effect on the chaotic behaviour of the dynamical system is investigated in this paper. The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos. As an example, for the Duffing system, we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos, and by combining figures, we discuss the influences of the amplitude, intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately. Finally, numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincaré map.

关 键 词：Melnikov theory bounded noise Lyapunov exponent Poincaré map 

分 类 号：O415.5[理学—理论物理]