具三阶段结构的非自治单种群模型正周期解的存在性  

Existence of positive periodic solution of a nonautonomous single species model with three stage structure

作　　者：梁志清[1] 陈兰荪[2] 

机构地区：[1]玉林师范学院数学与计算机科学系,广西玉林537000 [2]中国科学院数学研究所,北京100080

出　　处：《华中师范大学学报（自然科学版）》2005年第2期149-153,共5页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(10171106).

摘　　要：建立一类具三个阶段结构的非自治单种群模型:x′1(t)=a(t)x3(t-τ)-b1(t)x1(t)-c(t)x1(t),x′2(t)=c(t)x1(t)-d2(t)x2(t)-e(t)x2(t)-θ(t)x22(t),x′3(t)=e(t)x2(t)-f(t)x3(t).利用重合度理论中的延拓定理研究该模型的正周期解的存在性,得到了正周期解存在的充分条件.<Abstrcat> This paper establishes a nonautonomous single species model with three stage structure:x′_1(t)=a(t)x_3(t-τ)-b_1(t)x_1(t)-c(t)x_1(t),x′_2(t)=c(t)x_1(t)-d_2(t)x_2(t)-e(t)x_2(t)-θ(t)x\+2_2(t),x′_3(t)=e(t)x_2(t)-f(t)x_3(t).By using a continuation theorem based on coincidence degree theory, it studies the existence of positive solution of the model and obtains sufficient conditions for the existence of positive periodic solutions.

关 键 词：阶段结构 正周期解 重合度 种群模型 

分 类 号：O175.14[理学—数学]