Modeling and Cohesiveness Analysis of Midge Swarms

Abstract

Midges (Anarete pritchardi) coordinate their flight motions to form a cohesive group during swarming. In this paper, individual midge motion dynamics, sensing abilities, and flight rules are represented with a midge swarm model. The sensing accuracy and flight rule are adjusted so that the model produces trajectory behavior, and velocity, speed, and acceleration distributions, that are remarkably similar to those found in midge swarm experiments. Mathematical analysis of the validated swarm model shows that the distances between the midges' positions and the swarm position centroid, and the midges' velocities and the swarm velocity centroid, are ultimately bounded (i.e., eventually satisfy a bound expressed in terms of individual midge parameters). Likewise, the swarm position and velocity centroids are shown to be ultimately bounded. These analytical results provide insights into why the identified individual midge sensing characteristics and flight rule lead to cohesive swarm behavior.