Dynamics of a Stochastic Functional System for Wastewater Treatment

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 t...

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Main Authors: Xuehui Ji, Sanling Yuan
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/831573
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author Xuehui Ji
Sanling Yuan
author_facet Xuehui Ji
Sanling Yuan
author_sort Xuehui Ji
collection DOAJ
description 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.
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institution Kabale University
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language English
publishDate 2014-01-01
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series Abstract and Applied Analysis
spelling doaj-art-6e2a6d16b8f54968ae944bd033c4d75c2025-08-20T03:33:56ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/831573831573Dynamics of a Stochastic Functional System for Wastewater TreatmentXuehui Ji0Sanling Yuan1College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaThe 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.http://dx.doi.org/10.1155/2014/831573
spellingShingle Xuehui Ji
Sanling Yuan
Dynamics of a Stochastic Functional System for Wastewater Treatment
Abstract and Applied Analysis
title Dynamics of a Stochastic Functional System for Wastewater Treatment
title_full Dynamics of a Stochastic Functional System for Wastewater Treatment
title_fullStr Dynamics of a Stochastic Functional System for Wastewater Treatment
title_full_unstemmed Dynamics of a Stochastic Functional System for Wastewater Treatment
title_short Dynamics of a Stochastic Functional System for Wastewater Treatment
title_sort dynamics of a stochastic functional system for wastewater treatment
url http://dx.doi.org/10.1155/2014/831573
work_keys_str_mv AT xuehuiji dynamicsofastochasticfunctionalsystemforwastewatertreatment
AT sanlingyuan dynamicsofastochasticfunctionalsystemforwastewatertreatment