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