ON THE MAXIMAL LYAPUNOV EXPONENT FOR A REAL NOISE PARAMETRICALLY EXCITED CO-DIMENSION TWO BIFURCATION SYSTEM (Ⅱ)

Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (10): 1067-1074.

ON THE MAXIMAL LYAPUNOV EXPONENT FOR A REAL NOISE PARAMETRICALLY EXCITED CO-DIMENSION TWO BIFURCATION SYSTEM (Ⅱ)

刘先斌¹, 陈虬¹, 陈大鹏²

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

收稿日期:1998-05-29 出版日期:1999-10-18 发布日期:1999-10-18
基金资助:
the National Natural Science Foundation of China ( 19602016)

ON THE MAXIMAL LYAPUNOV EXPONENT FOR A REAL NOISE PARAMETRICALLY EXCITED CO-DIMENSION TWO BIFURCATION SYSTEM (Ⅱ)

Liu Xianbin¹, Chen Qiu¹, Chen Dapeng²

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

Received:1998-05-29 Online:1999-10-18 Published:1999-10-18
Supported by:
the National Natural Science Foundation of China ( 19602016)

摘要/Abstract

摘要： 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.

Abstract: 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.

中图分类号:

O211.63

刘先斌;陈虬;陈大鹏. ON THE MAXIMAL LYAPUNOV EXPONENT FOR A REAL NOISE PARAMETRICALLY EXCITED CO-DIMENSION TWO BIFURCATION SYSTEM (Ⅱ)[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(10): 1067-1074.

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 (English Edition), 1999, 20(10): 1067-1074.

[1]	吴臻;于志勇. LINEAR QUADRATIC NONZERO-SUM DIFFERENTIAL GAMES WITH RANDOM JUMP[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(8): 1034-1039 .
[2]	丁灯. A NOTE ON STOCHASTIC OPTIMAL CONTROL OF REFLECTED DIFFUSIONS WITH JUMPS[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(9): 1079-1090.
[3]	司徒荣;王越平. ON SOLUTIONS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS, WITH UNBOUNDED STOPPING TIMES AS TERMINAL AND WITH NON-LIPSCHITZ COEFFICIENTS, AND PROBABILISTIC INTERPRETATION OF QUASI-LINEAR ELLIPTIC TYPE INTEGRO-DIFFERENTIAL[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(6): 659-672.
[4]	刘先斌;陈大鹏;陈虬. ON THE MAXIMAL LYAPUNOV EXPONENT FOR A REAL NOISE PARAMETRICALLY EXCITED CO-DIMENSION TWO BIFURCATION SYSTEM (Ⅰ)[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(9): 967-978.

ON THE MAXIMAL LYAPUNOV EXPONENT FOR A REAL NOISE PARAMETRICALLY EXCITED CO-DIMENSION TWO BIFURCATION SYSTEM (Ⅱ)

ON THE MAXIMAL LYAPUNOV EXPONENT FOR A REAL NOISE PARAMETRICALLY EXCITED CO-DIMENSION TWO BIFURCATION SYSTEM (Ⅱ)

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

编辑推荐

Metrics

本文评价