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

Jaouad Danane and Delfim F. M. Torres ()
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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
Delfim F. M. Torres: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Mathematics, 2023, vol. 11, issue 7, 1-22

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.

Keywords: prey–predator system; stochastic persistence and extinction; logistic growth rate; Lévy noise; time delays (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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