Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:376

Article

Li, Xiaoyue^1,2  Gray, Alison³  Jiang, Daqing¹  Mao, Xuerong³ 

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Jilin Univ, Inst Math Sci, Changchun 130012, Peoples R China

[3] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

关键词: Brownian motion;    Stochastic differential equation;    Generalized Ito's formula;    Markov chain;    Stochastic permanence;   

DOI  :  10.1016/j.jmaa.2010.10.053

来源: Elsevier

【 摘 要 】

In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the population model. Finally, we illustrate our conclusions through two examples. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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