A Model of Flocking Using Sheaves

Joseph Geisz

Track: Full Paper (8 pages)

Keywords: Sheaves, Topology, Dynamical Systems, Flocking

TL;DR: A model of birds flocking can be described using the idea of a sheaf from algebraic topology.

Abstract: Sheaves have been used recently to model information on networks, such as the spread of opinions in a social network. Dynamical systems on networks model the evolving states of nodes on graphs. Using these lenses of sheaf theory and network dynamics, we explore a model of flocking. We describe from this perspective what it means for birds to come to consensus on flight velocities, and a system of ordinary differential equations (ODEs) that describes this consensus process. Then we couple these consensus dynamics with flight dynamics to describe a model of flocking. We include numerous visualizations of examples in 2 dimensions.

Submission Number: 28