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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
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    Full references (including those not matched with items on IDEAS)

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