具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为  

Dynamic Behavior of a Stochastic Predator Prey Model With the Gilpin-Ayala Growth

作　　者：陈乾君 蒋媛 刘子建 谭远顺 CHEN Qianjun;JIANG Yuan;LIU Zijian;TAN Yuanshun(College ofMathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,P.R.China)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074

出　　处：《应用数学和力学》2022年第4期453-468,共16页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11801047);重庆市自然科学基金(cstc2019jcyj-msxm2151);重庆市教委基金(KJQN201900707);重庆市研究生导师团队建设项目(JDDSTD201802);重庆市高校创新研究群体项目(CXQT21021)。

摘　　要：该文研究了一类具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为,证明了系统全局正解的存在性和唯一性,得到了灭绝性和持久性的充分条件.在此基础上,给出了控制捕食-食饵系统随机持久和灭绝的阈值,并且讨论了系统解的一些渐近性态.最后通过数值模拟,验证了结果的有效性.The dynamic behavior of a stochastic predator-prey model with the Gilpin-Ayala growth was studied. The existence and uniqueness of the global positive solution to the system were proved, and sufficient conditions for system extinction and persistence were obtained. On this basis, the thresholds for controlling the stochastic persistence and extinction of the predator-prey system were given, and some asymptotic behaviors of the solution were discussed. Finally,the effectiveness of the results was verified through numerical simulation.

关 键 词：Gilpin-Ayala增长 捕食-食饵模型 Markov状态切换 脉冲扰动 持久性 

分 类 号：O29[理学—应用数学]