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Stochastic dynamics of populations with refuge in polluted turbidostat

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  • Mu, Yu
  • Lo, Wing-Cheong

Abstract

Environmental pollution and random perturbation from the environment influence populations’ dynamics by alternating the habitat structure. To avoid disasters above or threats from predators, populations have self-defensive strategies such as camouflage or using a refuge. A turbidostat model with toxicant and prey refuge under the deterministic and stochastic environments is investigated in this work. We first analyze the positive solution’s existence and uniqueness under the effect of shelter and stochastic perturbation. We further determine the sufficient conditions of extinction and permanence for each population with the impact of toxicant, prey refuge under the stochastic environment. Our results reveal the dynamics of populations under the influence of the factors above. Several numerical examples are provided to verify the theoretical analysis and simulate the effect of the phenomena above in the population dynamics for both deterministic and stochastic cases.

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  • Mu, Yu & Lo, Wing-Cheong, 2021. "Stochastic dynamics of populations with refuge in polluted turbidostat," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003179
    DOI: 10.1016/j.chaos.2021.110963
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    References listed on IDEAS

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    1. Lv, Xuejin & Meng, Xinzhu & Wang, Xinzeng, 2018. "Extinction and stationary distribution of an impulsive stochastic chemostat model with nonlinear perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 273-279.
    2. Feifei Bian & Wencai Zhao & Yi Song & Rong Yue, 2017. "Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input," Complexity, Hindawi, vol. 2017, pages 1-18, December.
    3. Mengnan Chi & Wencai Zhao, 2019. "Dynamical Analysis of Two-Microorganism and Single Nutrient Stochastic Chemostat Model with Monod-Haldane Response Function," Complexity, Hindawi, vol. 2019, pages 1-13, March.
    4. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    5. Yajie Li & Xinzhu Meng, 2019. "Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-15, February.
    6. Yu Mu & Zuxiong Li & Huili Xiang & Hailing Wang, 2019. "Dynamical Analysis of a Stochastic Multispecies Turbidostat Model," Complexity, Hindawi, vol. 2019, pages 1-18, January.
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    Cited by:

    1. Yousef Alnafisah & Moustafa El-Shahed, 2022. "Stochastic Analysis of a Hantavirus Infection Model," Mathematics, MDPI, vol. 10(20), pages 1-15, October.

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