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Survival analysis of stochastic single-species population models in polluted environments

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  • Liu, Meng
  • Wang, Ke

Abstract

This paper reports on the behaviors of single species models with and without pollution. We consider three basic models, one is deterministic, and others are stochastic. We first obtained the acute thresholds between local extinction and (stochastic) weakly persistent in the mean for population respectively. Then we study the attainability of population size 0 for the stochastic cases and show that a randomized non-autonomous logistic equation will be stochastic permanent under some conditions. Finally, we introduce some numerical simulink graphics to illustrate our main results.

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  • Liu, Meng & Wang, Ke, 2009. "Survival analysis of stochastic single-species population models in polluted environments," Ecological Modelling, Elsevier, vol. 220(9), pages 1347-1357.
    • Handle: RePEc:eee:ecomod:v:220:y:2009:i:9:p:1347-1357
    DOI: 10.1016/j.ecolmodel.2009.03.001
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.
    2. Liu, Qun & Chen, Qingmei, 2015. "Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 52-67.
    3. Lan, Guijie & Wei, Chunjin & Zhang, Shuwen, 2019. "Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 828-842.
    4. Karim, Md Aktar Ul & Aithal, Vikram & Bhowmick, Amiya Ranjan, 2023. "Random variation in model parameters: A comprehensive review of stochastic logistic growth equation," Ecological Modelling, Elsevier, vol. 484(C).
    5. Liu, Yuting & Shan, Meijing & Lian, Xinze & Wang, Weiming, 2016. "Stochastic extinction and persistence of a parasite–host epidemiological model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 586-602.
    6. Zhao, Yu & Yuan, Sanling & Zhang, Qimin, 2015. "Numerical solution of a fuzzy stochastic single-species age-structure model in a polluted environment," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 385-396.
    7. Jiang, Daqing & Zhang, Qiumei & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Periodic solution for a stochastic non-autonomous competitive Lotka–Volterra model in a polluted environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 276-287.

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