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Maximal Lyapunov exponent of a co-dimension two bifurcation system excited by a white noise |
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| Authors: | X.B. Liu K.M. Liew |
| Affiliation: | a Nanyang Centre for Supercomputing and Visualisation, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore b Institute of Vibration Engineering Research, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210014, China c School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore |
| Abstract: | In this paper, we evaluate the maximal Lyapunov exponent for a co-dimension two bifurcation system, which is on a three-dimensional central manifold and is subjected to a parametric excitation by a white noise. Through a perturbation method, we obtain the explicit asymptotic expressions of the maximal Lyapunov exponent for three cases, in which different forms of the coefficient matrix that are included in the noise excitation term are assumed. |
| Keywords: | Maximal Lyapunov exponent Diffusion process Singular point FPK equation |
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