带交叉扩散与自扩散项的捕食-食饵模型正解的局部分歧  

The local bifurcation for a kind of prey-predator model with cross-diffusion and self-diffusion

作　　者：容跃堂[1] Rong Yuetang(School of Science, Xi′an Polytechnic University, Xi′an 710048, China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纯粹数学与应用数学》2018年第4期355-362,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金数学天元基金项目(11626182)

摘　　要：在Dirichlet第一初值边界条件下,研究了一类带交叉扩散与自扩散项的Variable-Territory捕食-食饵模型平衡态正解的存在性问题.利用极大值原理和分歧理论给出对应的平衡态方程正解的先验估计及其局部分歧解的存在性条件.This paper concerns the existence of positive solutions for a predator-prey model with cross-diffusion and self-diffusion and Variable-Territory type prey harvesting under homogeneous Dirichlet boundary conditions.By the maximum principle,a priori estimate of positive solutions are obtained and by Crandall-Rabinowitz bifurcation theory,the existence of positive solutions to a local bifurcation is proved.

关 键 词：捕食-食饵 交叉扩散与自扩散 正解 局部分歧 

分 类 号：O175.26[理学—数学]