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Abstract and Applied Analysis
Volume 2014, Article ID 831573, 18 pages
http://dx.doi.org/10.1155/2014/831573
Research Article

Dynamics of a Stochastic Functional System for Wastewater Treatment

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 20 January 2014; Accepted 2 February 2014; Published 24 March 2014

Academic Editor: Weiming Wang

Copyright © 2014 Xuehui Ji and Sanling Yuan. 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

The dynamics of a delayed stochastic model simulating wastewater treatment process are studied. We assume that there are stochastic fluctuations in the concentrations of the nutrient and microbes around a steady state, and introduce two distributed delays to the model describing, respectively, the times involved in nutrient recycling and the bacterial reproduction response to nutrient uptake. By constructing Lyapunov functionals, sufficient conditions for the stochastic stability of its positive equilibrium are obtained. The combined effects of the stochastic fluctuations and delays are displayed.