具有避难所的Leslie-Gower捕食系统的时空分歧  

Spatiotemporal bifurcation of a Leslie-Gower predator-prey system with prey refuge

作　　者：连彤 李艳玲[1] LIAN Tong;LI Yanling(College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《纺织高校基础科学学报》2019年第1期44-49,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金面上项目(61672021)

摘　　要：研究一类修正的具有食饵避难所的Leslie-Gower捕食-食饵模型。给出该模型非常数解的全局吸引子和持续共存性。得到该模型正平衡解的局部渐近稳定性,并通过构造Lyapunov函数得出正平衡解全局稳定的充分条件。利用分歧理论,以d为分歧参数,讨论了此模型在一维空间区域上的Hopf分歧与稳态分歧。A modified Leslie-Gower predator-prey model with prey refuge is investigated.The global attractor and uniform persistence of the nonconstant solutions are given.The local asymptotic stability of the positive equilibrium is obtained,and by constructing a Lyapunov function,the sufficient conditions for the global asymptotic stability of the positive equilibrium are derived.By regarding d as the bifurcation parameter,the Hopf and steady state bifurcation for the model in the one-dimension space case are discussed by means of the bifurcation theory.

关 键 词：Leslie-Gower模型 稳定性 HOPF分歧 稳态分歧 

分 类 号：O175.26[理学—数学]