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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. 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).
    2. 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).
    3. 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).
    4. 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).

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