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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 423154, 11 pages
http://dx.doi.org/10.1155/2013/423154
Research Article

Asymptotic Behavior of a Chemostat Model with Stochastic Perturbation on the Dilution Rate

1College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2Mathematics, FEIS, Swinburne University of Technology, P.O. Box 218 (H38) Hawthorn, VIC 3122, Australia

Received 4 October 2012; Revised 1 January 2013; Accepted 4 January 2013

Academic Editor: Ivanka Stamova

Copyright © 2013 Chaoqun Xu 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 present a stochastic simple chemostat model in which the dilution rate was influenced by white noise. The long time behavior of the system is studied. Mainly, we show how the solution spirals around the washout equilibrium and the positive equilibrium of deterministic system under different conditions. Furthermore, the sufficient conditions for persistence in the mean of the stochastic system and washout of the microorganism are obtained. Numerical simulations are carried out to support our results.