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Abstract and Applied Analysis
Volume 2014, Article ID 149801, 10 pages
http://dx.doi.org/10.1155/2014/149801
Research Article

Pattern Formation in a Bacterial Colony Model

1School of Mathematics, Wenzhou University, Wenzhou 325000, China
2Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610041, China
3School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China
4Department of Mathematics, Hubei Minzu University, Enshi, Hubei 445000, China

Received 2 January 2014; Accepted 8 February 2014; Published 23 March 2014

Academic Editor: Kaifa Wang

Copyright © 2014 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 investigate the spatiotemporal dynamics of a bacterial colony model. Based on the stability analysis, we derive the conditions for Hopf and Turing bifurcations. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by parameters in the model and find that the model dynamics exhibit a diffusion controlled formation growth to spots, holes and stripes pattern replication, which show that the bacterial colony model is useful in revealing the spatial predation dynamics in the real world.