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<p>In this paper, we develop and analyze two stochastic chemostat models incorporating discrete delays. For the first model, we assume the washout rate <i>D</i>(<i>t</i>) satisfies the mean-reverting Ornstein–Uhlenbeck process, while the other one satisfies the Black–Karasinski process. For both systems, we establish the existence and uniqueness of global positive solutions under biologically meaningful initial values. Then, we establish sufficient conditions for microbial population extinction and persistence in two systems. Finally, we provide some numerical examples to illustrate theoretical results and to compare the effects of two stochastic processes.</p>

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A comparison between mean-reverting Ornstein–Uhlenbeck process and Black–Karasinski process for a stochastic chemostat model with discrete delay

  • 期刊论文

  • 发表日期：

    2025年7月19日

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  • Dafei Shi,
  • Xiaofeng Zhang,
  • Rong Yuan

摘要

In this paper, we develop and analyze two stochastic chemostat models incorporating discrete delays. For the first model, we assume the washout rate D(t) satisfies the mean-reverting Ornstein–Uhlenbeck process, while the other one satisfies the Black–Karasinski process. For both systems, we establish the existence and uniqueness of global positive solutions under biologically meaningful initial values. Then, we establish sufficient conditions for microbial population extinction and persistence in two systems. Finally, we provide some numerical examples to illustrate theoretical results and to compare the effects of two stochastic processes.