Moment Lyapunov exponent for three-dimensional system under real noise excitation
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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 wordsmoment Lyapunov exponent perturbation method real noise diffusion process Fourier series
Chinese Library ClassificationO322 O324
2010 Mathematics Subject Classification60J70 70K20 70L05 74H60
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