Nabet, Benjamin (Princeton Univ.), Leonard, Naomi (Princeton Univ.), Couzin, Iain (Princeton Univ.), Levin, Simon (Princeton Univ.)

Leadership in Animal Group Motion: A Bifurcation Analysis

Scheduled for presentation during the Mini-Symposium "Cooperative Control" (FrA08), Friday, July 28, 2006, 11:15−11:40, Room I

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 25, 2024

Abstract

Animals move in groups when they forage or migrate, and it is known that the decisions they make on how to move depend on social interactions among group members. In previous work by Couzin et al., the mechanisms of decision-making and leadership were investigated by simulation. In this paper an animal is modeled as a particle moving in the plane at constant speed. It satisfies a first-order differential equation, where the heading rate of each particle is designed to be the sum of an attraction to the direction of, e.g., food and the possibly competing attraction to align itself with other particles. This model is similar to models used for cooperative control of engineered multi-agent systems. The paper studies the global phase space for the model by computing equilibria and proving stability and bifurcations.