IDEAS home Printed from https://ideas.repec.org/a/hin/complx/4873290.html
   My bibliography  Save this article

Dynamic Analysis of Stochastic Lotka–Volterra Predator-Prey Model with Discrete Delays and Feedback Control

Author

Listed:
  • Jinlei Liu
  • Wencai Zhao

Abstract

In this paper, a stochastic Lotka–Volterra predator-prey model with discrete delays and feedback control is studied. Firstly, the existence and uniqueness of global positive solution are proved. Further, we investigate the asymptotic property of stochastic system at the positive equilibrium point of the corresponding deterministic model and establish sufficient conditions for the persistence and extinction of the model. Finally, the correctness of the theoretical derivation is verified by numerical simulations.

Suggested Citation

  • Jinlei Liu & Wencai Zhao, 2019. "Dynamic Analysis of Stochastic Lotka–Volterra Predator-Prey Model with Discrete Delays and Feedback Control," Complexity, Hindawi, vol. 2019, pages 1-15, November.
  • Handle: RePEc:hin:complx:4873290
    DOI: 10.1155/2019/4873290
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/4873290.pdf
    Download Restriction: no

    File URL: http://downloads.hindawi.com/journals/8503/2019/4873290.xml
    Download Restriction: no

    File URL: https://libkey.io/10.1155/2019/4873290?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Meng, Xinzhu & Li, Fei & Gao, Shujing, 2018. "Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 701-726.
    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. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Guodong & Meng, Xinzhu, 2019. "Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    2. Dongmei Yuan & Yuzhen Bai, 2019. "Stability of Traveling Wave Fronts for a Three Species Predator-Prey Model with Nonlocal Dispersals," Complexity, Hindawi, vol. 2019, pages 1-15, December.
    3. Dezhao Li & Huidong Cheng & Yu Liu, 2019. "Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback Control," Complexity, Hindawi, vol. 2019, pages 1-13, November.
    4. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    5. Mu, Yu & Lo, Wing-Cheong, 2021. "Stochastic dynamics of populations with refuge in polluted turbidostat," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    6. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    7. Lei Fu & Hongwei Yang, 2019. "An Application of (3+1)-Dimensional Time-Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves," Complexity, Hindawi, vol. 2019, pages 1-15, August.
    8. Liu, Qun & Jiang, Daqing, 2020. "Threshold behavior in a stochastic SIR epidemic model with Logistic birth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    9. Rong Liu & Guirong Liu, 2018. "Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    10. Ruiqing Shi & Ting Lu & Cuihong Wang, 2019. "Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response," Complexity, Hindawi, vol. 2019, pages 1-13, August.
    11. Guo, Xiaoxia & Zhu, Chunjuan & Ruan, Dehao, 2019. "Dynamic behaviors of a predator–prey model perturbed by a complex type of noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1024-1037.
    12. Zhou, Baoquan & Jiang, Daqing & Han, Bingtao & Hayat, Tasawar, 2022. "Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 15-44.
    13. Zhu, Guanghu & Chen, Sixing & Shi, Benyun & Qiu, Hongjun & Xia, Shang, 2019. "Dynamics of echinococcosis transmission among multiple species and a case study in Xinjiang, China," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 103-109.
    14. Yuke Zhang & Xinzhu Meng, 2022. "Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    15. Chen, Xingzhi & Xu, Xin & Tian, Baodan & Li, Dong & Yang, Dan, 2022. "Dynamics of a stochastic delayed chemostat model with nutrient storage and Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    16. Fan, Kuangang & Zhang, Yan & Gao, Shujing & Chen, Shihua, 2020. "A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    17. Jin, Xihua & Jia, Jianwen, 2020. "Qualitative study of a stochastic SIRS epidemic model with information intervention," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    18. Chen, Xingzhi & Tian, Baodan & Xu, Xin & Zhang, Hailan & Li, Dong, 2023. "A stochastic predator–prey system with modified LG-Holling type II functional response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 449-485.
    19. He, Lingyun & Banihashemi, Seddigheh & Jafari, Hossein & Babaei, Afshin, 2021. "Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    20. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:4873290. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.