| Chaotic motion of the dynamical system under both additive and multiplicative noise excitations |
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| 引用本文： | 李秀春,徐 伟,李瑞红. Chaotic motion of the dynamical system under both additive and multiplicative noise excitations[J]. 中国物理 B, 2008, 17(2): 557-568 |
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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, NorthwesternPolytechnicalUniversity, Xi'an 710072, China;Department of Applied Mathematics, NorthwesternPolytechnicalUniversity, Xi'an 710072, China;Department of Applied Mathematics, NorthwesternPolytechnicalUniversity, Xi'an 710072, China |
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| 基金项目： | Project supported by the NationalNatural Science Foundation ofChina (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： | 2007-09-07 |
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 Li Rui-Hong |
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| Affiliation: | Department of Applied Mathematics, NorthwesternPolytechnicalUniversity, Xi'an 710072, China |
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| Abstract: | With both additive and multiplicative noise excitations, the effecton the chaotic behaviour of the dynamical system is investigated inthis paper. The random Melnikov theorem with the mean-squarecriterion that applies to a type of dynamical systems is analysed inorder to obtain the conditions for the possible occurrence of chaos.As an example, for the Duffing system, we deduce its concreteexpression for the threshold of multiplicative noise amplitude forthe rising of chaos, and by combining figures, we discuss theinfluences of the amplitude, intensity and frequency of both boundednoises on the dynamical behaviour of the Duffing system separately.Finally, numerical simulations are illustrated to verify thetheoretical analysis according to the largest Lyapunov exponent andPoincar'{e} map. |
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| Keywords: | Melnikov theory bounded noise Lyapunov exponent Poincar'{e} map |
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