On the maximal lyapunov exponent for a real noise parametrically excited co-dimension two bifurcation system (II)
- 28 Downloads
For a co-dimension two bifurcation system on a three-dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a linear filter system-a zeromean stationary Gaussian diffusion process which satisfies detailed balance condition. By means of the asymptotic analysis approach given by L. Arnold and the expression of the eigenvalue spectrum of Fokker-Planck operator, the asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are obtained.
Key wordsreal noise parametric excitation co-dimension two bifurcation detailed balance FPK equation singular boundary maximal Lyapunov exponent solvability condition
Unable to display preview. Download preview PDF.
- Ito K, McKean H P, Jr.Diffusion Processes and Their Sample Paths[M]. New York: Springer-Verlag, 1965.Google Scholar
- Karlin S, Taylor H M.A Second Course in Stochastic Processes [M]. New York: Academic Press, 1981.Google Scholar
- Liu Xianbin. Bifurcation behavior of stochastic mechanics system and its variational method[D]. Ph. D. Thesis. Chengdu: Southwest Jiaotong University, 1995. (in Chinese)Google Scholar
- Zhu Weiqiu.Stochastic Vibration[M]. Beijing: Science Press, 1992. (in Chinese)Google Scholar
- Arnold L, Wihstutz V.Lyapunov Exponents[M].Lecture Notes in Mathematics, 1186, Berlin, Springer-Verlag, 1986.Google Scholar