Positive Steady States of a Predator-prey System with Monod-Haldane Functional Response and Cross-diffusion

摘要

In this paper,we consider a strongly coupled partial differential equation system with Monod-Haldane functional response in a bounded domain with no flux boundary condition.Some priori estimates for steady states solutions are obtained by Harnack Inequality and Maximum Principle.A number of existence and non-existence results concerning non-constant positive steady-states of the system were proved.In particular,we demonstrate that cross-diffusion can create patterns when the corresponding system without cross-diffusion fails.