Modeling and Analyzing Large Swarms with Covert Leaders

In this paper, we analyze general models of large swarms with covert leaders. A covert leader is an individual who acts on additional information but is treated like all other individuals in the swarm. We concentrate our efforts on behavior driven by three-zone swarming, and present a new nonlinear model in which a leader will respond more strongly to additional information when the swarm is less dense. Conversely, leaders in denser regions behave more like followers. Linear stability analysis shows that the growth or decay of perturbations in an infinite, uniform swarm depends on the strength of attraction relative to repulsion and orientation. Understanding general systems like this has a wide range of applications in ecology, sociology and wireless robotics.