Research Article Permanence and Periodic Solution of Predator-Prey System with Holling Type Functional Response and Impulses

In biomathematics, many mathematical models have been established to describe the relationships between species and the outer environment, and the connections between different species. Among the relationships between the species living in the same outer environment, the predator-prey theory plays an important and fundamental role. The dynamic relationship between predators and their prey has long been one of the dominant theses in both ecology and mathematical ecology. Many excellent works have been done for the Lotka-Volterra type predator-prey system, for example, see [1–12]. In many situations, especially when predators have to search for food, a suitable general predatorprey theory is based on the so called ratio-dependent theory. Accordingly, researchers have proposed many ratio-dependent response functions. In [13], Holling suggested that there are three functional responses of the predator which usually are called Holling type I, Holling type II, and Holling type III. The type III response is typical of predators showing learning behavior, and