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

Our study focuses on analyzing the behavior of a stochastic predator-prey model with a time delay and logistic growth of prey, influenced by Levy 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.

Automated summary

Our study focuses on the behavior analysis of a stochastic predator-prey model with a time delay and logistic growth of prey under the influence of Levy noise. We establish the existence, uniqueness, and boundedness of a positive solution that spans globally. We explore the conditions for extinction and identify criteria for persistence. Numerical simulations validate our theoretical findings and illustrate the dynamics of the stochastic delayed predator-prey model based on different criteria.