I report here on a series of joint works with Alessandro Zilio about systems of predators interacting with a single prey. We analyze the situation of predators like wolves that can divide up into several hostile packs. The questions 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 that arise in this context. Mathematically, we focus on the analysis of stationary states, stability issues, and the asymptotics of the system when the competition parameter becomes unbounded. This system bears some similarities with models arising in multi-phase Bose-Einstein condensates.