Dynamic Behaviors of a Holling-type Predator-Prey System with Impulsive Immigration on the Predator

In this paper, we are concerned with the dynamic behaviors of a Holling-type predator-prey ystem with impulsive immigration on the predator. Holling functional response is x(p)/a + x(p), where a and p are positive parameters and 1 < p <2. This paper proves that the predator-prey system is always permanent. Finally, by means of numerical simulation, we illustrate that with increasing of the amount of the immigration the system experiences process of chaos attractor -> periodic halfing cascades -> cycle. This case is different from the previous works.