一类捕食-食饵模型共存解的存在性  

The existence of coexistence solutions of a predator-prey model

作　　者：魏欢 杨文彬 李艳玲[1] WEI Huan;YANG Wen-bin;LI Yan-ling(School of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710062,Shaanxi,China;School of Science,Xi'an University of Posts and Telecommunications,Xi'an 710121,Shaanxi,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 [2]西安邮电大学理学院,陕西西安710121

出　　处：《西北师范大学学报（自然科学版）》2018年第1期9-15,共7页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(61672021);陕西省教育厅专项科研计划项目(16JK1710)

摘　　要：研究一类捕食-食饵模型在齐次Dirichlet边值条件下的共存解.首先,利用极值原理和Young不等式得到正平衡态解的先验估计;其次,通过计算不动点指数,结合锥上的拓扑度理论和谱分析方法论讨了平衡态方程存在正解的充分必要条件,以及共存解对参数的依赖性;最后,以食饵的死亡率作为分歧参数,利用局部分歧定理证明了发自半平凡解的局部分支的存在性.The coexistence solutions of a predator-prey model with homogeneous Dirichlet boundary value conditions are studied.Firstly,by using the principle of extremum and the Young inequality,a priori estimate of positive equilibrium solution is given.Secondly,the sufficient and necessary conditions for the existence of positive solutions to equilibrium equation are discussed through the fixed-point index,topological degree theory and spectral analysis methods.Finally,taking the death rate as the bifurcation parameter,the existence of positive solution to this system is derived by making use of local bifurcation theory.

关 键 词：捕食-食饵模型 共存解 不动点指数 拓扑度理论 局部分歧 

分 类 号：O175.25[理学—数学]