Stability of a stochastic logistic model under regime switching

被引：0
作者：
Meng Liu
Li Yu
机构：
[1] Huaiyin Normal University,School of Mathematical Science
[2] Northeast Normal University,School of Mathematics and Statistics
[3] Harbin Far East Institute of Technology,Department of Basic
来源：
Advances in Difference Equations | / 2015卷
关键词：
logistic equation; Markovian switching; stability; extinction; 60H10; 60H30; 92D25;
D O I：
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学科分类号：
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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