Abstract 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.
Received: 31 October 2006
Revised: 07 September 2007
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of
China (Grant Nos 10472091 and 10332030).
Cite this article:
Li Xiu-Chun(李秀春), Xu Wei(徐伟), and Li Rui-Hong(李瑞红) Chaotic motion of the dynamical system under both additive and multiplicative noise excitations 2008 Chin. Phys. B 17 557
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