| Chaotic motion of the dynamical system under both additive and multiplicative noise excitations |
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| 作者姓名： | 李秀春 徐 伟 李瑞红 |
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| 作者单位： | Department of Applied Mathematics, Northwestern
Polytechnical
University, Xi'an 710072, China;Department of Applied Mathematics, Northwestern
Polytechnical
University, Xi'an 710072, China;Department of Applied Mathematics, Northwestern
Polytechnical
University, Xi'an 710072, China |
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| 基金项目： | Project supported by the National
Natural Science Foundation of
China (Grant Nos 10472091 and 10332030). |
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| 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.
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| 关 键 词： | Melnikov理论 有界噪音 动力学系统 混沌理论 |
| 收稿时间： | 2006-10-31 |
| 修稿时间： | 9/7/2007 12:00:00 AM |
Chaotic motion of the dynamical system under both additive and multiplicative noise excitations |
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| Li Xiu-Chun,Xu Wei and Li Rui-Hong.Chaotic motion of the dynamical system under both additive and multiplicative noise excitations[J].Chinese Physics B,2008,17(2):557-568. |
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| Authors: | Li Xiu-Chun Xu Wei and Li Rui-Hong |
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| Institution: | Department of Applied Mathematics, Northwestern
Polytechnical
University, Xi'an 710072, China |
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| 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
Poincar\'{e} map. |
| |
| Keywords: | Melnikov theory bounded noise Lyapunov exponent Poincar\'{e} map |
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