This paper is concerned with a modified Leslie-Gower and Holling-type II two-predator one-prey model with Lévy 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.
Keywords: Lévy jumps; extinction; persistence in the mean; two-predator one-prey model.