Stochastic stability of quasi-partially integrable and non-resonant Hamiltonian systems under parametric excitations of combined Gaussian and Poisson white noises

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• 作者：Weiyan Liu (1)
  Weiqiu Zhu (2)
  Wantao Jia (1)
  Xudong Gu (3)
  
• 关键词：Quasi ; partially integrable Hamiltonian system ; Combined Gaussian and Poisson white noise excitations ; Asymptotic Lyapunov stability with probability one ; The largest Lyapunov exponent
• 刊名：Nonlinear Dynamics
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：77
• 期：4
• 页码：1721-1735
• 全文大小：449 KB
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• 作者单位：Weiyan Liu (1)
  Weiqiu Zhu (2)
  Wantao Jia (1)
  Xudong Gu (3)
  
  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi鈥檃n聽, 710072, China
  2. Department of Mechanics, National Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou聽, 310027, China
  3. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi鈥檃n聽, 710072, China
  
• ISSN：1573-269X

文摘

The asymptotic Lyapunov stability with probability one of multi-degree-of freedom quasi-partially integrable and non-resonant Hamiltonian systems subject to parametric excitations of combined Gaussian and Poisson white noises is studied. First, the averaged stochastic differential equations for quasi partially integrable and non-resonant Hamiltonian systems subject to parametric excitations of combined Gaussian and Poisson white noises are derived by means of the stochastic averaging method and the stochastic jump-diffusion chain rule. Then, the expression of the largest Lyapunov exponent of the averaged system is obtained by using a procedure similar to that due to Khasminskii and the properties of stochastic integro-differential equations. Finally, the stochastic stability of the original quasi-partially integrable and non-resonant Hamiltonian systems is determined approximately by using the largest Lyapunov exponent. An example is worked out in detail to illustrate the application of the proposed method. The good agreement between the analytical results and those from digital simulation show that the proposed method is effective.