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Applied Mathematics and Mechanics

, Volume 20, Issue 10, pp 1067–1074 | Cite as

On the maximal lyapunov exponent for a real noise parametrically excited co-dimension two bifurcation system (II)

  • Liu Xianbin
  • Chen Qiu
  • Chen Dapeng
Article
  • 28 Downloads

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.

Key words

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

CLC number

O211.63 

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1999

Authors and Affiliations

  • Liu Xianbin
    • 1
  • Chen Qiu
    • 1
  • Chen Dapeng
    • 2
  1. 1.Institute of Applied Mechanics & EngineeringSouthwest Jiatong UniversityChengduP R China
  2. 2.Department of Engineering MechanicsSouthwest Jiaotong UniversityChengduP R China

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