EXISTENCE AND UNIQUENESS OF THE POSITIVE STEADY STATE SOLUTION FOR A LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH A CROWDING TERM  

作　　者：Xianzhong ZENG Lingyu LIU Weiyuan XIE 曾宪忠;刘玲妤;谢伟圆(School of Mathematics and Computing Science,Hunan University of Science and Technology,Xiangtan 411201,China)

机构地区：[1]School of Mathematics and Computing Science,Hunan University of Science and Technology,Xiangtan 411201,China

出　　处：《Acta Mathematica Scientia》2020年第6期1961-1980,共20页数学物理学报（B辑英文版）

基　　金：the Hunan Provincial Natural Science Foundation of China(2019JJ40079,2019JJ50160);the Scientific Research Fund of Hunan Provincial Education Department(16A071,19A179);the National Natural Science Foundation of China(11701169)。

摘　　要：This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation.We obtain a critical value λ1^D(Ω0),and demonstrate that the existence of the predator inΩ0 only depends on the relationship of the growth rateμof the predator and λ1^D(Ω0),not on the prey.Furthermore,whenμ<λ1^D(Ω0),we obtain the existence and uniqueness of its positive steady state solution,while whenμ≥λ1^D(Ω0),the predator and the prey cannot coexist inΩ0.Our results show that the coexistence of the prey and the predator is sensitive to the size of the crowding regionΩ0,which is different from that of the classical Lotka-Volterra predator-prey model.

关 键 词：Lotka-Volterra predator-prey model crowding term critical value COEXISTENCE 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]