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<p>This paper deals with a stochastic model of the so-called Anaerobic Model number 2. Here the maximal growth rate of the acidogenic microorganisms is affected by a white noise in environment. As far as the mathematical analysis of this model is concerned, we first use the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(It\hat{o}\)</EquationSource> </InlineEquation> formula to investigate the existence and uniqueness of the global positive solution. Then, we explore and derive the conditions of persistence and extinction of the microorganisms. Finally, by performing some numerical simulations, we illustrate the theoretical results obtained.</p>

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A Two-Step Stochastic Model of Anaerobic Digestion

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月1日

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  • Martial Patrick Tale Solefack,
  • Calvin Tadmon

摘要

This paper deals with a stochastic model of the so-called Anaerobic Model number 2. Here the maximal growth rate of the acidogenic microorganisms is affected by a white noise in environment. As far as the mathematical analysis of this model is concerned, we first use the \(It\hat{o}\) formula to investigate the existence and uniqueness of the global positive solution. Then, we explore and derive the conditions of persistence and extinction of the microorganisms. Finally, by performing some numerical simulations, we illustrate the theoretical results obtained.