Modeling the herd prey response to individualistic predators attacks

In this paper, we consider predators hunting on prey gathered in groups and in such way exhibiting the possibility of reducing the predators pressure. To model this feature, however, we depart from the Holling type II (HTII) response function, in that we assume that a sufficiently large set of prey could respond to individualistic attacks and therefore induce the predator to renounce. The basic idea is described at first in a simple two-populations predator-prey system. It is then expanded considering the generalist predators to deal with two prey. In the first case, both are gathered in herds, and in the second one, one of the two instead behaves individualistically. The net outcome is an enhanced survival for the prey with respect to both the herding cases without and with predators feeding satiation (i.e., using the HTII response).