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

作　　者：李胜宏 刘先斌 

机构地区：[1]State Key Laboratory of Mechanics and Control for Mechanical Structures,College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics [2]School of Mathematics and Physics,Jiangsu University of Science and Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第5期613-626,共14页应用数学和力学（英文版）

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

摘　　要：The pth moment Lyapunov exponent of a two-codimension bifurcation systern 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.The pth moment Lyapunov exponent of a two-codimension bifurcation systern 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.

关 键 词：moment Lyapunov exponent perturbation method real noise diffusion process Fourier series 

分 类 号：O211.6[理学—概率论与数理统计] O19[理学—数学]