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Threshold dynamics in a stochastic chemostat model under regime switching

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  • Wang, Liang
  • Jiang, Daqing
  • Feng, Tao

Abstract

A stochastic chemostat model in random environments that is driven by Brownian motions and subjected to Markov regime switching is considered. The new break-even concentration, i.e., critical value between persistence in mean and extinction is explored for the microorganism species. Moreover, sufficient conditions for ergodicity and positive recurrence is established by using stochastic Lyapunov analysis. Numerical simulations are accomplished to verify the analytical results.

Suggested Citation

  • Wang, Liang & Jiang, Daqing & Feng, Tao, 2022. "Threshold dynamics in a stochastic chemostat model under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    • Handle: RePEc:eee:phsmap:v:599:y:2022:i:c:s0378437122003338
    DOI: 10.1016/j.physa.2022.127454
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    References listed on IDEAS

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    1. Campillo, F. & Joannides, M. & Larramendy-Valverde, I., 2011. "Stochastic modeling of the chemostat," Ecological Modelling, Elsevier, vol. 222(15), pages 2676-2689.
    2. Emel Savku & Gerhard-Wilhelm Weber, 2018. "A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 696-721, November.
    3. Peng, Shige & Zhu, Xuehong, 2006. "Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 370-380, March.
    4. Weber, Gerhard-Wilhelm & Defterli, Ozlem & Alparslan Gök, SIrma Zeynep & Kropat, Erik, 2011. "Modeling, inference and optimization of regulatory networks based on time series data," European Journal of Operational Research, Elsevier, vol. 211(1), pages 1-14, May.
    5. Khasminskii, R.Z. & Zhu, C. & Yin, G., 2007. "Stability of regime-switching diffusions," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1037-1051, August.
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    Cited by:

    1. Sheng Wang & Lijuan Dong, 2023. "Stochastic Dynamics of a Hybrid Delay Food Chain Model with Harvesting and Jumps in a Polluted Environment," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-31, December.
    2. Junfeng Zhao & Bingshuo Wang & Wei Li & Dongmei Huang & Vesna Rajic, 2025. "Dynamical Properties of a Stochastic Tumor–Immune System with Impulsive Perturbations and Regime Switching," Mathematics, MDPI, vol. 13(6), pages 1-29, March.
    3. Sheng Wang & Lijuan Dong, 2024. "Dynamics of a Stochastic Regime-Switching Four-Species Food Chain Model with Distributed Delays and Harvesting," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-15, September.

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