On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co-Dimension Two Bifurcation System(Ⅱ)

Liu Xianbin; Chen Qiu; Chen Dapeng

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Liu Xianbin, Chen Qiu, Chen Dapeng. On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co-Dimension Two Bifurcation System(Ⅱ)[J]. Applied Mathematics and Mechanics, 1999, 20(10): 997-1003.

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On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co-Dimension Two Bifurcation System(Ⅱ)

1.
Institute of Applied Mechanics & Engineering, Southwest Jiaotong University, Chengdu 610031, P R China;
2.
Department of Engineering Mechanics, Southwest Jiaotong University, Chengdu 610031, P R China

Received Date: 1998-05-29
Publish Date: 1999-10-15

Abstract

Abstract

Foraco-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.
- real noise,
- parametric excitation,
- co-dimension two bifurcation,
- detailed balance,
- FPK equation,
- singular boundary,
- maximal Lyapunov exponent,
- solvability condition

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References(11)

References

[1]	Ito K,McKean H P,Jr.Diffusion Processes and Their Sample Paths[M].New York:Springer-Verlag,1965.
[2]	Karlin S,Taylor H M.A Second Course in Stochastic Processes[M].New York:Academic Press,1981.
[3]	刘先斌.随机力学系统的分叉行为与变分方法研究[D].博士学位论文.成都:西南交通大学,1995.
[4]	刘先斌,陈虬,陈大鹏.非线性随机动力系统的稳定性和分岔研究[J].力学进展,1996,26(4):437～452.
[5]	刘先斌,陈虬,孙训方.白噪声参激一类余维2分岔系统研究[J].力学学报,1997,29(5):563～572.
[6]	朱位秋.随机振动[M].北京:科学出版社,1992.
[7]	Lin Y K,Cai G Q.Stochastic stability of nonlinear systems[J].Int J Nonlinear Mech,1994,29(4):539～555.
[8]	Ariaratnam S T, Xie W C.Lyapunov exponents and stochastic stability of two-dimensional parametrically excited random systems[J].ASME J Appl Mech,1993,60(5):677～682.
[9]	Arnold L,Wihstutz V.Lyapunov Exponents[M].Lecture Notes in Mathematics,1186,Berlin:Springer-Verlag,1986.
[10]	Arnold L,Papanicolaou G,Wihstutz V.Asympototic analysis of the Lyapunov exponents and rotation numbers of the random oscilltor and applications[J].SIAM J Appl Math,1986,46(3):427～450.
[11]	刘先斌,陈大鹏,陈虬.实噪声参激一类余维2分叉系统的最大Lyapunov指数(Ⅰ)[J].应用数学和力学,1999,20(9):902～913.