Exploring the Optimality of a Limited View Angle in the Two-Dimensional Vicsek Model

Abstract

Collective behavior emerges from local interactions in a group, has been observed in many natural systems, and is of significant interests for engineering applications. The Vicsek model is a mathematical tool to study collective alignment in a group of self-propelled particles based on local interaction, which has been well-studied in the literature for its simple algorithm and complex global behaviors. Several studies show that particles reach alignment faster when the directionality of particle interaction is restricted by an optimal view angle. This result seems counterintuitive, since each particle is expected to get more information through omnidirectional interaction. This work seeks to explore the possible causes of this optimal view angle by studying interaction dynamics in Vicsek model with restricted view angle through numerical simulation.