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

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Abstract

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.

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Authors and Affiliations

  1. Department of Applied Mechanics and Engineering, Southwest Jiaotong University, 610031, Chengdu, P R China

    Liu Xianbin

  2. Institute of Engineering Science, Southwest Jiaotong University, 610031, Chengdu, P R China

    Chen Dapeng

Authors
  1. Liu Xianbin
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  2. Chen Dapeng
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  3. Chen Qiu
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Foundation item: the National Natural Science Foundation of China (19602016)

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Xianbin, L., Dapeng, C. & Qiu, C. On the maximal Lyapunov exponent for a real noise parametrically excited Co-dimension two bifurcation system (I). Appl Math Mech 20, 967–978 (1999). https://doi.org/10.1007/BF02459059

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  • DOI: https://doi.org/10.1007/BF02459059

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