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Abstract and Applied Analysis
Volume 2014, Article ID 510671, 9 pages
http://dx.doi.org/10.1155/2014/510671
Research Article

Minimal Wave Speed of Bacterial Colony Model with Saturated Functional Response

1School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2College of Mathematics & Computer Science, Yangtze Normal University, Chongqing 408100, China

Received 12 January 2014; Accepted 24 February 2014; Published 31 March 2014

Academic Editor: Weiming Wang

Copyright © 2014 Tianran Zhang and Qingming Gou. 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

By considering bacterium death and general functional response we develop previous model of bacterial colony which focused on the traveling speed of bacteria. The minimal wave speed for our model is expressed by parameters and the necessary and sufficient conditions for traveling wave solutions (TWSs) are given. To prove the existence of TWSs, an auxiliary system is introduced and the existence of TWSs for this auxiliary system is proved by Schauder’s fixed point theorem. The limit arguments show the existence of TWSs for original system. By introducing negative one-sided Laplace transform, we prove the nonexistence of TWSs.