Swarm shape and its dynamics in a predator-swarm model

Abstract

We consider a particle predator-swarm model introduced in [1]. In the continuum limit of many prey particles, we develop a numerical method which tracks the boundary of the swarm. We use this method to explore the variety and complexity of swarm shapes. We also consider a special limiting case where the predator is moving inside an infinite sea of prey. Two subcases are studied: one where the predator is moving along a straight line, and another where the predator is moving in a circle. We observe various topological changes in the swarm shape as the predator speed increases, such as the appearance of an infinite tail for a predator moving in a straight line when its speed is large enough.