The dynamical properties of a complex Ivlev-type predator-prey system with impulsive effect

In this paper,a complex Ivlev-type predator-prey system with impulsive effect is built. Conditions for extinction of mid-lever predator are given. By using Floquet Theory,we show that the lowest-level prey(pest) and the mid-level predator (natural enemy)extinction periodic solution is unstable,while the mid-level predator eradication periodic solution is stable, we prove the system is permanent if the impulsive period is larger than one critical value. At last we show the influence of the impulsive perturbation by using numerical analysis.