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Stochastic Characteristics and Optimal Control for a Stochastic Chemostat Model with Variable Yield

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  • Rong Yan
  • Shulin Sun

Abstract

In this paper, a stochastic chemostat model with variable yield and Contois growth function is investigated. The yield coefficient depends on the limiting nutrient, and the environmental noises are given by independent standard Brownian motions. First, the existence and uniqueness of global positive solution are proved. Second, by using stochastic Lyapunov function, Itô’s formula, and some important inequalities, stochastic characteristics for the stochastic model are studied, including the extinction of micro-organism, the strong persistence in the mean of micro-organism and, the existence of a unique stationary distribution of the stochastic model. Third, the necessary condition of an optimal stochastic control for the stochastic model is established by Hamiltonian function. In addition, some numerical simulations are carried out to illustrate the theoretical results and the influence of the variable yield on the microorganism.

Suggested Citation

  • Rong Yan & Shulin Sun, 2020. "Stochastic Characteristics and Optimal Control for a Stochastic Chemostat Model with Variable Yield," Complexity, Hindawi, vol. 2020, pages 1-18, April.
    • Handle: RePEc:hin:complx:5065172
    DOI: 10.1155/2020/5065172
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    Cited by:

    1. Lili Kong & Luping Li & Shugui Kang & Fu Chen, 2023. "Dynamic Behavior of a Stochastic Avian Influenza Model with Two Strains of Zoonotic Virus," Mathematics, MDPI, vol. 11(19), pages 1-21, October.
    2. Zhang, Xiaofeng & Yuan, Rong, 2021. "Forward attractor for stochastic chemostat model with multiplicative noise," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. Zhang, Xiaofeng & Yuan, Rong, 2021. "A stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function," Applied Mathematics and Computation, Elsevier, vol. 394(C).

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