The Existence and Non-Existence of Positive Steady State Solutions for a Cross-Diffusion Predator-Prey Model with Holling Type Ⅱ Functional Response  

作　　者：Shuping CAO Li-na ZHANG 

机构地区：[1]Department of Mathematics and Statistics,Northwest Normal University,Gansu 730070,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2021年第4期383-392,共10页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11761063).

摘　　要：In this paper,we consider the positive steady state solutions of a predator-prey model with Holling type Ⅱfunctional response and cross-diffusion,where two cross-diffusion rates represent the tendency of prey to keep away from its predator and the tendency of the predator to chase its prey,respectively.Applying the fixed point index theory,some sufficient conditions for the existence of positive steady state solutions are established.Furthermore,the non-existence of positive steady state solutions is studied.

关 键 词：predator-prey model Holling typeⅡfunctional response CROSS-DIFFUSION coexistence states 

分 类 号：O175[理学—数学] Q141[理学—基础数学]