Positive Steady State Solutions of a Diffusive Leslie-Gower Predator-Prey Model with Holling Type II Functional Response and Cross-Diffusion

Authors

Jun Zhou
Chan-Gyun Kim, William & Mary
Junping Shi, William & Mary

Document Type

Article

Department/Program

Mathematics

Journal Title

Discrete and Continuous Dynamical Systems

Pub Date

2014

Volume

34

Issue

9

First Page

3875

Abstract

In this paper we consider a diffusive Leslie Gower predator prey model with Holling type II functional response and cross-diffusion under zero Dirichlet boundary condition. By using topological degree theory, bifurcation theory, energy estimates and asymptotic behavior analysis, we prove the existence, uniqueness and multiplicity of positive steady states solutions under certain conditions on the parameters.

Recommended Citation

Zhou, Jun; Kim, Chan-Gyun; and Shi, Junping, Positive Steady State Solutions of a Diffusive Leslie-Gower Predator-Prey Model with Holling Type II Functional Response and Cross-Diffusion (2014). Discrete and Continuous Dynamical Systems, 34(9), 3875-3899.
https://doi.org/10.3934/dcds.2014.34.3875

DOI

https://doi.org/10.3934/dcds.2014.34.3875