Stability of a stochastic logistic model under regime switching

被引：5
|
作者：
Liu, Meng [1 ,2 ]
Yu, Li [3 ]
机构：
[1] Huaiyin Normal Univ, Sch Mat Sci, Huaian 223300, Peoples R China
[2] NE Normal Univ, Sch Math & Stat, Changchun 130022, Peoples R China
[3] Harbin Far East Inst Technol, Dept Basic, Harbin 150025, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2015年
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
logistic equation; Markovian switching; stability; extinction; ASYMPTOTIC PROPERTIES; POPULATION; EXTINCTION; DYNAMICS; EQUATION; SYSTEMS; SIMULATIONS; PERSISTENCE; ENVIRONMENT;
D O I：
10.1186/s13662-015-0666-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this letter, we consider a stochastic generalized logistic equation with Markovian switching. We obtain a critical value which has the property that if the critical value is negative, then the trivial solution of the model is stochastically globally asymptotically stable; if the critical value is positive, then the solution of the model is positive recurrent and has a unique ergodic stationary distribution. We find out that the critical value has a close relationship with the stationary probability distribution of the Markov chain.
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页数：9
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