The Stochastic stability of a Logistic model with Poisson white noise

doi:10.1088/1674-1056/20/3/030501

Abstract The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised Itô differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species.

Keywords: Poisson white noise It? formula Lyapunov exponent stochastic bifurcation

Received: 15 September 2010
Revised: 25 October 2010
Accepted manuscript online:

PACS:

05.10.Gg

(Stochastic analysis methods)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10872165 and 10932009).

Cite this article:

Duan Dong-Hai(段东海), Xu Wei(徐伟), Su Jun(苏军), and Zhou Bing-Chang(周丙常) The Stochastic stability of a Logistic model with Poisson white noise 2011 Chin. Phys. B 20 030501

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