Dynamical Behaviors for a Predator-Prey System with State-Dependent Impulsive Effects

With some theory about continuous and impulsive dynamical system, an impulsive model based on a special predator-prey system is considered. We assume that the impulsive effects occur when the density of the prey reaches a given value. For such a state-dependent impulsive system, the existence, uniqueness and orbital asymptotic stability of an order-1 periodic solution are discussed. Further, the existence of an order-2 periodic solution is also obtained, and persistence of the system is investigated.