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Dynamics of a Stochastic Functional System for Wastewater Treatment

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  • Xuehui Ji
  • Sanling Yuan

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.

Suggested Citation

  • Xuehui Ji & Sanling Yuan, 2014. "Dynamics of a Stochastic Functional System for Wastewater Treatment," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:831573
    DOI: 10.1155/2014/831573
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    References listed on IDEAS

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    1. Jiao, Jianjun & Yang, Xiaosong & Chen, Lansun & Cai, Shaohong, 2009. "Effect of delayed response in growth on the dynamics of a chemostat model with impulsive input," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2280-2287.
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