Dynamics Behavior of a Stochastic Predator-Prey Model with Stage Structure for Predator and L\''{e}vy Jumps

In order to study the effects of external environmental noise on the interaction dynamics between predator and prey populations, in this paper, we develop a predator-prey model with the stage structure for predator and L$\acute{\rm e}$vy noise. By constructing an appropriate Lyapunov function, we first prove that the proposed model exists the uniqueness of global positive solution. Then, we analyze the persistence and extinction of the proposed model. Finally, we perform some numerical simulations to verify the correctness of the theoretical results.