The Stochastic stability of a Logistic model with Poisson white noise

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

中国物理B ›› 2011, Vol. 20 ›› Issue (3): 30501-030501.doi: 10.1088/1674-1056/20/3/030501

The Stochastic stability of a Logistic model with Poisson white noise

段东海¹, 徐伟¹, 周丙常¹, 苏军²

(1)Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; (2)School of Science, Xi'an University of Science and Technology, Xi'an 710054, China

收稿日期:2010-09-15 修回日期:2010-10-25 出版日期:2011-03-15 发布日期:2011-03-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10872165 and 10932009).

The Stochastic stability of a Logistic model with Poisson white noise

Duan Dong-Hai(段东海)^a)†, Xu Wei(徐伟)^a), Su Jun(苏军)^b), and Zhou Bing-Chang(周丙常)^a)

^a Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; ^b School of Science, Xi'an University of Science and Technology, Xi'an 710054, China

Received:2010-09-15 Revised:2010-10-25 Online:2011-03-15 Published:2011-03-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10872165 and 10932009).

摘要/Abstract

摘要： 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 It? 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.

关键词: Poisson white noise, It? formula, Lyapunov exponent, stochastic bifurcation

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.

Key words: Poisson white noise, It? formula, Lyapunov exponent, stochastic bifurcation

中图分类号: (Stochastic analysis methods)

05.10.Gg

段东海, 徐伟, 苏军, 周丙常. The Stochastic stability of a Logistic model with Poisson white noise[J]. 中国物理B, 2011, 20(3): 30501-030501.

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[J]. Chin. Phys. B, 2011, 20(3): 30501-030501.

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The Stochastic stability of a Logistic model with Poisson white noise

The Stochastic stability of a Logistic model with Poisson white noise

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