State transitions and the continuum limit for a 2D interacting, self-propelled particle system

Authored by Andrea L Bertozzi, Maria R D'Orsogna, Yao-Li Chuang, Daniel Marthaler, Lincoln S Chayes

Date Published: 2007

DOI: 10.1016/j.physd.2007.05.007

Sponsors: United States Office of Naval Research (ONR) United States National Science Foundation (NSF)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the self-propulsion and interaction potential parameters. In this paper, we utilize a procedure which connects a class of individual -based models to their continuum formulations and determine criteria for the validity of the latter. H-stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions. We perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual -based one. (c) 2007 Elsevier B.V. All rights reserved.
Tags
collective motion Emergent properties Model Aggregation Populations Phase-transition Fish schools Swarms Individual behavior Stability analysis