Analisi di un modello predatore preda con difesa di gruppo e attacco di gruppo

In this thesis I propose a mathematical predator-prey model in which predators cooperate to hunt prey and prey behave as a group while defend- ing from predators' attack. This model can be considered as a mixture of two existing models: the first describing group defense (see [7]) and the latter describing pack hunting (see [4]). I consider a particular functional response among the ones proposed in [7] to describe prey cooperation, and I make a simpler assumption as regards pack hunting than the one made in [4]. I make a comparison between the new model and the previous ones to understand what kind of behavior can arise when pack hunting and group defense work together. For instance, the prey carrying capacity is a locally stable equilibrium for all parameters values. I point out which are the criti- cal points of the model: the compensation between group defense and pack hunting and the importance of a stable carrying capacity. At the end I propose a generalization of this model.