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:
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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