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Applied Mathematics and Mechanics

, Volume 34, Issue 5, pp 613–626 | Cite as

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

  • Sheng-hong Li (李胜宏)
  • Xian-bin Liu (刘先斌)Email author
Article
  • 94 Downloads

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.

Key words

moment Lyapunov exponent perturbation method real noise diffusion process Fourier series 

Chinese Library Classification

O322 O324 

2010 Mathematics Subject Classification

60J70 70K20 70L05 74H60 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sheng-hong Li (李胜宏)
    • 1
    • 2
  • Xian-bin Liu (刘先斌)
    • 1
    Email author
  1. 1.State Key Laboratory of Mechanics and Control for Mechanical Structures, College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjingP. R. China
  2. 2.School of Mathematics and PhysicsJiangsu University of Science and TechnologyZhenjiangJiangsu Province, P. R. China

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