The moment Lyapunov exponent of a co-dimension two bifurcation system driven by non-Gaussian colored noise

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• 作者：Jiancheng Wu^a ; ^b ; ^{slxy_wu@126.com" class="auth_mail" title="E-mail the corresponding author} ; Xuan Li^a ; ^{lix@nuaa.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xianbin Liu^a ; ^{xbliu@nuaa.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Moment Lyapunov exponent ; Perturbation method ; Green's function ; Non-Gaussian colored noise ; Monte Carlo simulation
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 August 2016
• 年：2016
• 卷：286
• 期：Complete
• 页码：189-200
• 全文大小：996 K

文摘

In the present paper, based on the concept of the pth moment Lyapunov exponent, the stochastic stability of a typical co-dimension two bifurcation system, that is on a three-dimensional center manifold and possesses two pure imaginary eigenvalues and one zero-eigenvalue and is excited by a non-Gaussian colored noise, is investigated. The non-Gaussian colored noise is treated as an Ornstein–Uhlenbeck process by means of the path-integral approach. Based on the perturbation approach and the Green's functions method, the second differential eigenvalue equation which governing the moment Lyapunov exponent is established. By solving the eigenvalue problem, the weak noise asymptotic expansions for the finite pth moment Lyapunov exponent are obtained, and which matches the approximation of the numerical Monte Carlo simulations. Finally, the conclusions are given.