Applied Mathematics and Mechanics

, Volume 20, Issue 9, pp 967–978 | Cite as

On the maximal Lyapunov exponent for a real noise parametrically excited Co-dimension two bifurcation system (I)

  • Liu Xianbin
  • Chen Dapeng
  • Chen Qiu


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

Key words

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

CLC number



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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1999

Authors and Affiliations

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

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