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Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process

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  • Ayoubi, Tawfiqullah
  • Bao, Haibo

Abstract

The persistence and extinction (PE) are interesting topics in mathematics. This research analyzed PE of stochastic Logistic equations (SLE) by incorporating the Ornstein-Uhlenbeck process (SLOP) and stochastic delay Logistic equation (SDLE) by incorporating the Ornstein-Uhlenbeck process (SLDOP). Firstly, we proved that SLOP and SLDOP have positive solutions. Likewise, for stochastic permanence (SP), weak persistence in the mean (WPM), non-persistence in the mean (NPM) and extinction, the sufficient conditions are established for SLOP and SLDOP. Subsequently, for numerical simulation we used 4-stage stochastic Runge-Kutta (SRK4) to illustrate the effectiveness of the results.

Suggested Citation

  • Ayoubi, Tawfiqullah & Bao, Haibo, 2020. "Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304252
    DOI: 10.1016/j.amc.2020.125465
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    References listed on IDEAS

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    1. Zhangzhi Wei & Zheng Wu & Ling Hu & Lianglong Wang, 2018. "Persistence and Extinction of a Stochastic Modified Bazykin Predator-Prey System with Lévy Jumps," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-7, April.
    2. Liu, Meng & Deng, Meiling & Du, Bo, 2015. "Analysis of a stochastic logistic model with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 169-182.
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    Cited by:

    1. Alfifi, H.Y., 2021. "Stability and Hopf bifurcation analysis for the diffusive delay logistic population model with spatially heterogeneous environment," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    2. Su, Tan & Yang, Qing & Zhang, Xinhong & Jiang, Daqing, 2023. "Stationary distribution, extinction and probability density function of a stochastic SEIV epidemic model with general incidence and Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    3. Wang, Haile & Zuo, Wenjie & Jiang, Daqing, 2023. "Dynamical analysis of a stochastic epidemic HBV model with log-normal Ornstein–Uhlenbeck process and vertical transmission term," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    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).

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