Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2010; 47(2): 251-261

Printed March 1, 2010

https://doi.org/10.4134/BKMS.2010.47.2.251

Copyright © The Korean Mathematical Society.

Stationary patterns for a predator-prey model with Holling type III response function and cross-diffusion

Jia Liu and Zhigui Lin

Jiangsu Polytechnic University and Yangzhou University

Abstract

This paper deals with a predator-prey model with Holling type III response function and cross-diffusion subject to the homogeneous Neumann boundary condition. We first give a priori estimates (positive upper and lower bounds) of positive steady states. Then the non-existence and existence results of non-constant positive steady states are given as the cross-diffusion coefficient is varied, which means that stationary patterns arise from cross-diffusion.

Keywords: predator-prey model, stationary patterns, existence

MSC numbers: 35J55