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Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species

Author

Listed:
  • Jaouad Danane

    (Laboratory of Systems, Modelization and Analysis for Decision Support, National School of Applied Sciences (ENSA), University Hassan 1st of Settat, Berrechid B.P 218, Morocco
    These authors contributed equally to this work.)

  • Delfim F. M. Torres

    (Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
    These authors contributed equally to this work.)

Abstract

Our study focuses on analyzing the behavior of a stochastic predator–prey model with a time delay and logistic growth of prey, influenced by Lévy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive solution that spans globally. Subsequently, we explore the conditions under which extinction occurs, and identify adequate criteria for persistence. Finally, we validate our theoretical findings through numerical simulations, which also helps illustrate the dynamics of the stochastic delayed predator–prey model based on different criteria.

Suggested Citation

  • Jaouad Danane & Delfim F. M. Torres, 2023. "Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species," Mathematics, MDPI, vol. 11(7), pages 1-22, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1595-:d:1107287
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    References listed on IDEAS

    as
    1. Akdim, Khadija & Ez-zetouni, Adil & Danane, Jaouad & Allali, Karam, 2020. "Stochastic viral infection model with lytic and nonlytic immune responses driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    2. Liu, Meng & Bai, Chuanzhi & Deng, Meiling & Du, Bo, 2016. "Analysis of stochastic two-prey one-predator model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 176-188.
    3. Meng, Xin-You & Huo, Hai-Feng & Xiang, Hong & Yin, Qi-yu, 2014. "Stability in a predator–prey model with Crowley–Martin function and stage structure for prey," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 810-819.
    4. Yuanfu Shao & Weili Kong, 2022. "A Predator–Prey Model with Beddington–DeAngelis Functional Response and Multiple Delays in Deterministic and Stochastic Environments," Mathematics, MDPI, vol. 10(18), pages 1-25, September.
    5. Wu, Jian, 2018. "Stability of a three-species stochastic delay predator–prey system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 492-505.
    6. Zhang, Xinhong & Li, Wenxue & Liu, Meng & Wang, Ke, 2015. "Dynamics of a stochastic Holling II one-predator two-prey system with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 571-582.
    7. Shufen Zhao & Minghui Song, 2014. "A Stochastic Predator-Prey System with Stage Structure for Predator," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    Full references (including those not matched with items on IDEAS)

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