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- Publisher
- Springer Journals
- Copyright
- 2012 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
- ISSN
- 0567-7718
- eISSN
- 1614-3116
- DOI
- 10.1007/s10409-012-0013-y
- Publisher site
- See Article on Publisher Site
Abstract
Abstract In the present paper, the maximal Lyapunov exponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise. By using a perturbation method, the expressions of the invariant measure of a one-dimensional phase diffusion process are obtained for three cases, in which different forms of the matrix B, that is included in the noise excitation term, are assumed and then, as a result, all the three kinds of singular boundaries for one-dimensional phase diffusion process are analyzed. Via Monte-Carlo simulation, we find that the analytical expressions of the invariant measures meet well the numerical ones. And furthermore, the P-bifurcation behaviors are investigated for the one-dimensional phase diffusion process. Finally, for the three cases of singular boundaries for one-dimensional phase diffusion process, analytical expressions of the maximal Lyapunov exponent are presented for the stochastic bifurcation system.
Journal
"Acta Mechanica Sinica" – Springer Journals
Published: Apr 1, 2012