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

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.