中文摘要：

考虑种群增长率和种群内部竞争制约系数分别受到噪声扰动的两类随机非自治Logistic竞争种群系统,采用Markov切换的方式,研究这两类随机种群系统的持久性与灭绝性。通过构造Lyapunov函数方法,证明种群系统的静态分布,给出种群系统在切换状态下的持久生存、非平均持久生存和灭绝性的充分性判据。两个数值模拟支持了理论分析的结果。

英文摘要：

Two types of non-autonomous competitive Logistic systems in random environments,containing population growth rate and internal competition restriction coefficient disturbanced by noise,are considered. The persistance and extinction on two types of stochastic competitive Logistic systems are mainly studied by the way of Markov switching. By using Lyapunov function method,a stationary distribution of systems is investigated. Furthermore,some sufficient conditions for persistance,non- average persistent and extinction on systems are established in the swtich- state. Finally,numerical simulations are carried out to support the theoretical results.