交错扩散对具有Ivlev型功能反应的捕食模型共存解存在性的作用  

The effect of cross-diffusion on the existence of coexistence solutions for a predator-prey model with Ivlev-type functional response

作　　者：田旻 张丽娜 TIAN Min;ZHANG Li-na(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《云南大学学报（自然科学版）》2021年第1期11-16,共6页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11761063).

摘　　要：研究交错扩散对具有Ivlev型功能反应的捕食者−食饵模型共存解存在性的影响,其中交错扩散描述猎物追逐食饵以及食饵躲避猎物的情形.首先应用拓扑度理论与指数不动点定理得到共存解存在的充分条件,其次利用能量估计方法导出共存解不存在的充分条件.We study the effect of cross-diffusion on the existence of coexistence solutions for a predator-prey model with Ivlev type functional response,in which cross-diffusion describes the situation of predator chasing its prey and prey avoiding its predator.Firstly,the sufficient conditions for the existence of coexistence solutions are obtained by using the topological degree theory and the fixed point index theory.Secondly,the sufficient conditions for the nonexistence of coexistence solutions are derived by using the energy estimation method.

关 键 词：捕食者−食饵模型 Ivlev功能反应 交错扩散 共存解 

分 类 号：O175.26[理学—基础数学]