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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/831573 |
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| _version_ | 1849414102672211968 |
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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. |
| format | Article |
| id | doaj-art-6e2a6d16b8f54968ae944bd033c4d75c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |