Emergence of diverse collective behaviors from local topological perception

Modeling "social" interactions within a large population has proven to be a rich subject of study for a variety of scientific communities during the past few decades. Specifically, with the goal of predicting the macroscopic effects resulting from microscopic-scale endogenous as well as exogenous interactions, many emblematic models for the emergence of collective behaviors have been proposed. In this talk we present a dynamical model for generic crowds in which individual agents are aware of their local environment, i.e., neighboring agents and domain boundary features, and may seek static targets. Our model incorporates features common to many other "active matter'' models like collision avoidance, alignment among agents, and homing toward targets. However, it is novel in key respects: the model combines topological and metrical features in a natural manner based upon the local environment of the agent's Voronoi diagram. With only two parameters, it is shown to capture a wide range of collective behaviors that go beyond the more classical velocity consensus and group cohesion. The work presented here is joint with R. Choksi and J.C. Nave at McGill