In this lecture, I will discuss a model that aims at showing how certain predators form territories and packs. This model rests on basic principles of predators – prey interaction and competition. I will start by introducing the classical Lotka-Volterra model, describing predator – prey dynamics. This simple system is one of the cornerstones of mathematical ecology. Including spatial dependence and animal movement, one is led to a system of reaction-diffusion equations.

In this context I will present recent work in collaboration with Alessandro Zilio about an extension of the original Lotka-Volterra system. We analyze the situation of predators like wolves that can divide up into several hostile packs. The questions we address are to understand the conditions under which predators segregate into packs, whether there is an advantage to have such hostile packs, and to compare the various territory configurations thus emerging.