Moment Lyapunov exponent of three-dimensional system under bounded noise excitation

doi:10.1007/s10483-012-1570-9

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (5): 553-566.doi: https://doi.org/10.1007/s10483-012-1570-9

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Moment Lyapunov exponent of three-dimensional system under bounded noise excitation

Ci-jun FANG^1,2, Jian-hua YANG³, Xian-bin LIU¹

1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China;
2. School of Science, Hubei University of Technology, Wuhan 430068, P. R. China;
3. School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu Province, P. R. China

Received:2011-09-16 Revised:2012-02-16 Online:2012-05-10 Published:2012-05-10
Contact: Xian-bin LIU, Professor, Ph.D., E-mail: xbliu@nuaa.edu.cn E-mail:xbliu@nuaa.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11072107 and 91016022) and the Research Fund for the Doctoral Program of Higher Education of China (No. 20093218110003)

Abstract

Abstract: In the present paper, the moment Lyapunov exponent of a codimensional two-bifurcation system is evaluted, which is on a three-dimensional central manifold and subjected to a parametric excitation by the bounded noise. Based on the theory of random dynamics, the eigenvalue problem governing the moment Lyapunov exponent is established. With a singular perturbation method, the explicit asymptotic expressions and numerical results of the second-order weak noise expansions of the moment Lyapunov are obtained in two cases. Then, the effects of the bounded noise and the parameters of the system on the moment Lyapunov exponent and the stability index are investigated. It is found that the stochastic stability of the system can be strengthened by the bounded noise.

Key words: bounded noise, moment Lyapunov exponent, stability index

2010 MSC Number:

O324

Ci-jun FANG;Jian-hua YANG;Xian-bin LIU. Moment Lyapunov exponent of three-dimensional system under bounded noise excitation. Applied Mathematics and Mechanics (English Edition), 2012, 33(5): 553-566.

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Moment Lyapunov exponent of three-dimensional system under bounded noise excitation

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