具有时滞的非自治的捕食-食饵系统的全局吸引

具有时滞的非自治的捕食-食饵系统的全局吸引 Global Attractivity for Nonautonomous Predator-Prey System with Time Delay 张树文 ZHANG Shu-wen 1 1 2 3 4 first-author 陈兰荪 CHEN Lan-sun3 1 2 3 4 大连理工大学应用数学系 大连理工大学应用数学系 Department of Applied Mathematics, Dalian University of Technology Department of Applied Mathematics, Dalian University of Technology 中国科学院数学研究所,辽宁,大连,116024 中国科学院数学研究所,辽宁,大连,116024 Institute of Biomathematics, Anshan Normal University Institute of Biomathematics, Anshan Normal University 鞍山师范学院生物数学研究所 鞍山师范学院生物数学研究所 Institute of Mathematics, Chinese Academy of Sciences Institute of Mathematics, Chinese Academy of Sciences ,北京,100080 ,北京,100080 考虑一个具有离散时滞的非自治的捕食 食饵系统 .系统是由 3种群组成的 ,其中一个为捕食者 ,另两个为食饵种群 .本文的目的是给出时滞对系统的持续生存是无害的 ,从而确定了系统的周期解全局吸引的条件 . One of the most interesting topics in mathematical ecology concerns the permanence of ecological systems.In this paper,we consider a nonautonomous three-species（two-prey,one-predator） predator-prey Lotka-Volterra system with discrete delays.We get the ultimately lower and upper bounds for the positive solution by estimate of inequatity and constructing suitable persistemce functionals.If assuming environment varies periodly,we obtain the existence,uniqueness and global attractivity of positive periodic solution for periodic system by using fixed point theorem.Liapunov function and M-matrix theory.Further conditions are established for the permancnce of the populations and the global attractivity of positive periodic solution.These conditions is not complexity and acceptable.In addition,we also discuss the effect of delay permanence and positive periodic solution of the system.These results demonstrate that time delays are harmlas for uniform persistence of the populations and the existence of positive periodic solution. 时滞 全局吸引 捕食者食饵系统 time delays global attractivity predator-prey system O175.13 国家自然科学基金资助项目 （ 10 17110 6） 2003-03-01 2021-04-01 3