On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co-Dimension Two Bifurcation System(Ⅰ)

Liu Xianbin; Chen Dapeng; Chen Qiu

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Liu Xianbin, Chen Dapeng, Chen Qiu. On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co-Dimension Two Bifurcation System(Ⅰ)[J]. Applied Mathematics and Mechanics, 1999, 20(9): 902-912.

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On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co-Dimension Two Bifurcation System(Ⅰ)

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 Date: 1998-05-29
Rev Recd Date: 1999-04-15
Publish Date: 1999-09-15

Abstract

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

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References(24)

References

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