Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (9): 967-978.

• 论文 • 上一篇    下一篇

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

刘先斌1, 陈大鹏2, 陈虬1   

  1. 1. Department of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China;
    2. Institute of Engineering Science, Southwest Jiaotong University, Chengdu 610031, P. R. China
  • 收稿日期:1998-05-29 修回日期:1999-04-15 出版日期:1999-09-18 发布日期:1999-09-18
  • 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 (Ⅰ)

Liu Xianbin1, Chen Dapeng2, Chen Qiu1   

  1. 1. Department of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P. R. China;
    2. Institute of Engineering Science, Southwest Jiaotong University, Chengdu 610031, P. R. China
  • Received:1998-05-29 Revised:1999-04-15 Online:1999-09-18 Published:1999-09-18
  • Supported by:

    the National Natural Science Foundation of China(19602016)

摘要: For a real noise parametrically excited co-dimension two bifurcation system on a 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.

Abstract: For a real noise parametrically excited co-dimension two bifurcation system on a 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.

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