Stochastic Modeling of Three-Species Prey–Predator Model Driven by Lévy Jump with Mixed Holling-II and Beddington–DeAngelis Functional Responses

Abstract

This study examines the dynamics of a stochastic prey–predator model using a functional response function driven by Lévy noise and a mixed Holling-II and Beddington–DeAngelis functional response. The proposed model presents a computational analysis between two prey and one predator population dynamics. First, we show that the suggested model admits a unique positive solution. Second, we prove the extinction of all the studied populations, the extinction of only the predator, and the persistence of all the considered populations under several sufficient conditions. Finally, a special Runge–Kutta method for the stochastic model is illustrated and implemented in order to show the behavior of the two prey and one predator subpopulations.

Keywords

• prey–predator
• stochastic model
• Lévy jump
• Holling-II functional
• Beddington–DeAngelis functional
• Runge–Kutta method