Persistence and extinction of a modified Leslie-Gower Holling-type II two-predator one-prey model with Levy jumps

This paper is concerned with a modified Leslie-Gower and Holling-type II two-predator one-prey model with Levy jumps. First, we use an Ornstein-Uhlenbeck process to describe the environmental stochasticity and prove that there is a unique positive solution to the system. Moreover, sufficient conditions for persistence in the mean and extinction of each species are established. Finally, we give some numerical simulations to support the main results.

Automated summary

This paper investigates a modified Leslie-Gower and Holling-type II two-predator one-prey model with Levy jumps. An Ornstein-Uhlenbeck process is employed to capture the environmental stochasticity, and it is proved that a unique positive solution exists. Sufficient conditions for the persistence in the mean and extinction of each species are established, and numerical simulations are provided to support the main findings.