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

• Articles • Previous Articles     Next Articles

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)

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.

2010 MSC Number: 

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals