On the maximal Lyapunov exponent for a real noise parametrically excited Co-dimension two bifurcation system (I)
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For a real noise parametrically excited co-dimension two bifurcation system on three-dimensional central manifold, a model of enhanced generality is developed in the present paper by assuming the real noise to be an output of a linear filter system, namely, a zero-mean stationary Gaussian diffusion process that satisfies the detailed balance condition. On such basis, asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are established by use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum of Fokker-Planck operator.
Key wordsreal noise parametric excitation co-dimension two bifurcation detailed balance condition FPK equation singular boundary maximal Lyapunov exponent solvability condition
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- 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
- Liu Xianbin, Chen Qiu. Advances in the researches on stochastic stability and stochastic bifurcation [R]. Invited paper of MMM-VII, Shanghai 1997. (in Chinese)Google Scholar
- Arnold L.. Lyapunov exponents of nonlinear stochastic systems [A]. In:, F Ziegler, G I Schueller eds.Nonlinear Stochastic Dynamic Engrg Systems, Berlin, New York: Springer-Verlag, 1987, 181–203.Google Scholar
- Arnold L, Boxler P. Eigenvalues, bifurcation and center manifolds in the presence of noise [A]. In: C M Dafermos, G Ladas, G Papannicolaou eds,Differential Equations [M]. New York: Marcel Dekker Inc, 1990, 33–50.Google Scholar
- Kozin F.Stability of the Linear Stochaxtic Systems [M].Lecture Notes in Math,294. New York: Springer-Verlag, 1972, 186–229.Google Scholar
- Liu Xianbin, Chen Qiu, Sun Xunfang. On co-dimension 2 bifurcation system excited parametrically by white noise [J].Acta Mechanica Sinia, 1997,29(5) 563–572. (in Chinese)Google Scholar
- Zhu Weiqiu.Stochastic Vibration [M]. Beijing: Science Press, 1992. (in Chinese)Google Scholar