Moment Lyapunov exponent for three-dimensional system under real noise excitation |
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Authors: | Sheng-hong Li Xian-bin Liu |
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Institution: | 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;
2. School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, Jiangsu Province, P. R. China |
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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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Keywords: | moment Lyapunov exponent perturbation method real noise diffusion process Fourier series |
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