A Holling's predator-prey model with handling and searching predators

The goal of this paper is to explain how to derive the classical Rosenzweig-MacArthur model by using a model with two groups of predators in which we can separate the vital dynamic and consumption of prey to describe the behavior of the predators. This will be especially very convenient if we want to add an age or size structure to the predator population. As mentioned by Holling (without mathematical model), we divide the population of predators into the searching and the handling predators. In this article we study some properties of this model and conclude by proving that the model converges to the classical Rosenzweig-MacArthur model by using an appropriate rescaling. This convergence property is observed by using numerical simulations. We also apply this model to the Canadian snowshoe hares and the lynx.