State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System
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, in a definitive way, 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.
Cite
@article{arxiv.nlin/0606031,
title = {State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System},
author = {Yao-li Chuang and Maria R. D'Orsogna and Daniel Marthaler and Andrea L. Bertozzi and Lincoln S. Chayes},
journal= {arXiv preprint arXiv:nlin/0606031},
year = {2009}
}