Stationary patterns for a predator-prey model with Holling type III response function and cross-diffusion
Bull. Korean Math. Soc. 2010 Vol. 47, No. 2, 251-261
https://doi.org/10.4134/BKMS.2010.47.2.251
Printed March 1, 2010
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
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