Dynamics of a Leslie–Gower Holling-type II predator–prey system with Lévy jumps

This paper is concerned with a stochastic predator–prey system with modified Leslie–Gower and Holling-type II schemes with Lévy jumps. First, we prove there is a unique positive solution to the system with a positive initial value. Then we establish the sufficient conditions for stability in mean and extinction of the system. Finally, we introduce some numerical simulations to support the main results. The results shows that the Lévy jumps can change the properties of the population systems significantly.