具分布时滞和扩散的周期随机Logistic模型研究  

Analysis of a Periodic Stochastic Logistic Model with Distributed Delay and Dispersal

作　　者：王宏伟 董玲珍 WANG Hong-wei;DONG Ling-zhen(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《数学的实践与认识》2020年第22期284-296,共13页Mathematics in Practice and Theory

基　　金：山西省自然科学基金(2013011002-3)。

摘　　要：研究了一个具分布时滞和扩散的周期随机Logistic模型.利用Ito公式,首先证明了系统全局正解的存在性;进一步,分析了系统的灭绝和平均持久生存,给出了系统灭绝和平均持久生存的充分条件;然后利用Has’ minskii周期解理论,通过构造Lyapunov函数,证明了系统非平凡正周期解的存在性;最后,通过数值模拟验证了理论分析结果的正确性.In this paper,we study a periodic stochastic logistic model with distributed delay and dispersal,using the itO's formula,we first prove the existence of the global positive solution of the model;further,we analyze the extinction and persistence in the mean of the system.the sufficient conditions which guarantee the extinction and persistence in the mean of the system are obtained.then by using has'minskii theory about periodic solution and constructing the lyapunov function,it is proved that the model has a nontrivial positive periodic solution,finally,we verify the correctness of the theoretical analysis results by numerical simulation.

关 键 词：周期随机系统 分布时滞 全局正解 平均持久 非平凡周期解 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]