Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching
Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching
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政权转换下随机物流种群随机持久和灭绝的充分必要条件
DOI：
10.1016/j.jmaa.2010.10.053
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发表时间：
2011-04-01
影响因子：
1.3
通讯作者：
Mao, Xuerong
中科院分区：
文献类型：
--
作者：
Li, Xiaoyue;Gray, Alison;Mao, Xuerong
本文证明了在Markov链控制下的状态转换下的随机Logistic种群是随机持久的或随机灭绝的，并在一定的假设下得到了随机持久和随机灭绝的充要条件.在随机持久性的情况下，我们估计的平均时间的限制的样本路径的解决方案由两个常数有关的平稳概率分布的马尔可夫链和人口模型的子系统的参数。最后，我们通过两个例子来说明我们的结论。(C)2010年爱思唯尔公司All rights reserved.
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.