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Moment Lyapunov exponent for three-dimensional system under real noise excitation

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Abstract

The pth moment Lyapunov exponent of a two-codimension bifurcation system excited parametrically by a real noise is investigated. By a linear stochastic transformation, the differential operator of the system is obtained. In order to evaluate the asymptotic expansion of the moment Lyapunov exponent, via a perturbation method, a ralevant eigenvalue problem is obtained. The eigenvalue problem is then solved by a Fourier cosine series expansion, and an infinite matrix is thus obtained, whose leading eigenvalue is the second-order of the asymptotic expansion of the moment Lyapunov exponent. Finally, the convergence of procedure is numerically illustrated, and the effects of the system and the noise parameters on the moment Lyapunov exponent are discussed.

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210014, P. R. China

    Sheng-hong Li  (李胜宏) & Xian-bin Liu  (刘先斌)

  2. School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, 212003, Jiangsu Province, P. R. China

    Sheng-hong Li  (李胜宏)

Authors
  1. Sheng-hong Li  (李胜宏)
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  2. Xian-bin Liu  (刘先斌)
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Corresponding author

Correspondence to Xian-bin Liu  (刘先斌).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11072107, 91016022, and 11232007)

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Li, Sh., Liu, Xb. Moment Lyapunov exponent for three-dimensional system under real noise excitation. Appl. Math. Mech.-Engl. Ed. 34, 613–626 (2013). https://doi.org/10.1007/s10483-013-1695-8

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  • DOI: https://doi.org/10.1007/s10483-013-1695-8

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Chinese Library Classification

2010 Mathematics Subject Classification

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