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The moment Lyapunov exponent for a three-dimensional stochastic system

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  • Li, Xuan
  • Liu, Xianbin

Abstract

This paper presents a method, through which the pth moment stability of a linear multiplicative stochastic system, that is a linear part of a co-dimension two-bifurcation system upon a three-dimensional center manifold and is subjected to a parametric excitation by an ergodic real noise, is obtained. The excitation included is assumed to be an integrable function of an n-dimensional Ornstein–Uhlenbeck vector process that is the output of a linear filter system and both the strong mixing condition, which is the sufficient condition for the stochastic averaging method, and the delicate balance condition are removed in the present study. By using a perturbation method and the spectrum representations of both the Fokker Planck operator and its adjoint one of the linear filter system, the asymptotic expressions of the moment Lyapunov exponent are obtained, which match the numerical results well.

Suggested Citation

  • Li, Xuan & Liu, Xianbin, 2014. "The moment Lyapunov exponent for a three-dimensional stochastic system," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 40-47.
    • Handle: RePEc:eee:chsofr:v:68:y:2014:i:c:p:40-47
    DOI: 10.1016/j.chaos.2014.07.007
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