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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 147232, 10 pages
http://dx.doi.org/10.1155/2013/147232
Research Article

Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion

1Department of Mathematics, Wenzhou University, Wenzhou 325035, China
2Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610041, China
3College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
4Department of Mathematics, Hubei Minzu University, Enshi 445000, China

Received 29 August 2013; Revised 4 October 2013; Accepted 4 October 2013

Academic Editor: Massimiliano Ferrara

Copyright © 2013 Xinze Lian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.