The Existence and Non-Existence of Positive Steady State Solutions for a Cross-Diffusion Predator-Prey Model with Holling Type II Functional Response
Received:April 20, 2020  Revised:October 25, 2020
Key Word: predator-prey model   Holling type II functional response   cross-diffusion   coexistence states  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11761063).
Author NameAffiliation
Shuping CAO Department of Mathematics and Statistics, Northwest Normal University, Gansu 730070, P. R. China 
Li-na ZHANG Department of Mathematics and Statistics, Northwest Normal University, Gansu 730070, P. R. China 
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Abstract:
      In this paper, we consider the positive steady state solutions of a predator-prey model with Holling type II functional 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.
Citation:
DOI:10.3770/j.issn:2095-2651.2021.04.006
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