Abstract
We implement an ordinary differential equation model of predator-prey interactions with swarming behavior. We employ exponentially decaying interactions between the agents so that it is possible for the swarm to split into several groups or for the swarm to escape from the predator. We begin with an analysis of large groups of prey and show that there are several qualitatively different behaviors that depend on the relative strength and length scales of the attraction and repulsion between predator and prey. Introducing polar coordinates for the prey allows us to describe certain classes of symmetric configurations. The splitting of large swarms into smaller swarms of variable numbers of prey motivates our analysis of small groups of prey with differing attractiveness to the predator. In these reduced models we find a variety of oscillations such as the slow circling of prey relative to the predator as well as very complex quasi-periodic behavior.
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