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http://dx.doi.org/10.4134/BKMS.2010.47.2.251

STATIONARY PATTERNS FOR A PREDATOR-PREY MODEL WITH HOLLING TYPE III RESPONSE FUNCTION AND CROSS-DIFFUSION  

Liu, Jia (DEPARTMENT OF INFORMATION SCIENCE JIANGSU POLYTECHNIC UNIVERSITY)
Lin, Zhigui (SCHOOL OF MATHEMATICAL SCIENCE YANGZHOU UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.2, 2010 , pp. 251-261 More about this Journal
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;
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