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The moment Lyapunov exponent of a co-dimension two bifurcation system driven by non-Gaussian colored noise

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  • Wu, Jiancheng
  • Li, Xuan
  • Liu, Xianbin

Abstract

In the present paper, based on the concept of the pth moment Lyapunov exponent, the stochastic stability of a typical co-dimension two bifurcation system, that is on a three-dimensional center manifold and possesses two pure imaginary eigenvalues and one zero-eigenvalue and is excited by a non-Gaussian colored noise, is investigated. The non-Gaussian colored noise is treated as an Ornstein–Uhlenbeck process by means of the path-integral approach. Based on the perturbation approach and the Green's functions method, the second differential eigenvalue equation which governing the moment Lyapunov exponent is established. By solving the eigenvalue problem, the weak noise asymptotic expansions for the finite pth moment Lyapunov exponent are obtained, and which matches the approximation of the numerical Monte Carlo simulations. Finally, the conclusions are given.

Suggested Citation

  • Wu, Jiancheng & Li, Xuan & Liu, Xianbin, 2016. "The moment Lyapunov exponent of a co-dimension two bifurcation system driven by non-Gaussian colored noise," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 189-200.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:189-200
    DOI: 10.1016/j.amc.2016.04.001
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    References listed on IDEAS

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    1. Fuentes, M.A. & Wio, Horacio S. & Toral, Raúl, 2002. "Effective Markovian approximation for non-Gaussian noises: a path integral approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(1), pages 91-104.
    2. Bouzat, Sebastián & Wio, Horacio S., 2005. "New aspects on current enhancement in Brownian motors driven by non-Gaussian noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(1), pages 69-78.
    3. Fuentes, M.A. & Toral, Raúl & Wio, Horacio S., 2001. "Enhancement of stochastic resonance: the role of non Gaussian noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 114-122.
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