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Stationary distribution of a stochastic chemostat model with Beddington–DeAngelis functional response

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  • Cao, Zhongwei
  • Wen, Xiangdan
  • Su, Huishuang
  • Liu, Liya
  • Ma, Qiang

Abstract

In this paper, we study a stochastic chemostat model with Beddington–DeAngelis functional response. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of a unique ergodic stationary distribution to the model. The existence of a stationary distribution implies stochastic weak stability.

Suggested Citation

  • Cao, Zhongwei & Wen, Xiangdan & Su, Huishuang & Liu, Liya & Ma, Qiang, 2020. "Stationary distribution of a stochastic chemostat model with Beddington–DeAngelis functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    • Handle: RePEc:eee:phsmap:v:554:y:2020:i:c:s0378437120303095
    DOI: 10.1016/j.physa.2020.124634
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    References listed on IDEAS

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    1. Liu, Qun & Jiang, Daqing & Shi, Ningzhong, 2018. "Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 310-325.
    2. Campillo, F. & Joannides, M. & Larramendy-Valverde, I., 2011. "Stochastic modeling of the chemostat," Ecological Modelling, Elsevier, vol. 222(15), pages 2676-2689.
    3. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Nontrivial periodic solution of a stochastic non-autonomous SISV epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 837-845.
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