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Clustering conditions and the cluster formation process in a dynamical model of multidimensional attracting agents

Filip De Smet UGent and Dirk Aeyels UGent (2012) SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS. 11(1). p.392-415
abstract
We consider a multiagent clustering model where each agent belongs to a multidimensional space. We investigate its long term behavior, and we prove emergence of clustering behavior in the sense that the velocities of the agents approach asymptotic values, independently of the initial conditions; agents with equal asymptotic velocities are said to belong to the same cluster. We propose a set of relations governing these asymptotic velocities. These results are compared with results obtained earlier for the model with agents belonging to a one-dimensional space and are then explored for the case of an infinite number of agents. For the particular case of a spherically symmetric configuration of an infinite number of agents a rigorous analysis of the relations governing the asymptotic velocities is possible, assuming that a continuity property established for the finite case remains true for the infinite case. This leads to a characterization of the onset of cluster formation in terms of the evolution of the cluster size with varying coupling strength. A remarkable point is that the cluster formation process depends critically on the dimension of the agent state space; considering the cluster size as an order parameter, the cluster formation in the one-dimensional case may be seen as a second-order phase transition, while the multidimensional case is associated with a first-order phase transition. We provide bounds for the critical coupling strength at the onset of the cluster formation, and we illustrate the results with two examples in three dimensions.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
clustering, self-organization, phase transition, EVOLUTION, EQUATIONS, AGGREGATION, OSCILLATORS, BEHAVIOR, multiagent systems
journal title
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
SIAM J. Appl. Dyn. Syst.
volume
11
issue
1
pages
392 - 415
Web of Science type
Article
Web of Science id
000302237300014
JCR category
MATHEMATICS, APPLIED
JCR impact factor
1.453 (2012)
JCR rank
36/247 (2012)
JCR quartile
1 (2012)
ISSN
1536-0040
DOI
10.1137/100807855
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2120007
handle
http://hdl.handle.net/1854/LU-2120007
date created
2012-05-30 09:54:10
date last changed
2012-05-31 14:30:28
@article{2120007,
  abstract     = {We consider a multiagent clustering model where each agent belongs to a multidimensional space. We investigate its long term behavior, and we prove emergence of clustering behavior in the sense that the velocities of the agents approach asymptotic values, independently of the initial conditions; agents with equal asymptotic velocities are said to belong to the same cluster. We propose a set of relations governing these asymptotic velocities. These results are compared with results obtained earlier for the model with agents belonging to a one-dimensional space and are then explored for the case of an infinite number of agents. For the particular case of a spherically symmetric configuration of an infinite number of agents a rigorous analysis of the relations governing the asymptotic velocities is possible, assuming that a continuity property established for the finite case remains true for the infinite case. This leads to a characterization of the onset of cluster formation in terms of the evolution of the cluster size with varying coupling strength. A remarkable point is that the cluster formation process depends critically on the dimension of the agent state space; considering the cluster size as an order parameter, the cluster formation in the one-dimensional case may be seen as a second-order phase transition, while the multidimensional case is associated with a first-order phase transition. We provide bounds for the critical coupling strength at the onset of the cluster formation, and we illustrate the results with two examples in three dimensions.},
  author       = {De Smet, Filip and Aeyels, Dirk},
  issn         = {1536-0040},
  journal      = {SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS},
  keyword      = {clustering,self-organization,phase transition,EVOLUTION,EQUATIONS,AGGREGATION,OSCILLATORS,BEHAVIOR,multiagent systems},
  language     = {eng},
  number       = {1},
  pages        = {392--415},
  title        = {Clustering conditions and the cluster formation process in a dynamical model of multidimensional attracting agents},
  url          = {http://dx.doi.org/10.1137/100807855},
  volume       = {11},
  year         = {2012},
}

Chicago
De Smet, Filip, and Dirk Aeyels. 2012. “Clustering Conditions and the Cluster Formation Process in a Dynamical Model of Multidimensional Attracting Agents.” Siam Journal on Applied Dynamical Systems 11 (1): 392–415.
APA
De Smet, Filip, & Aeyels, D. (2012). Clustering conditions and the cluster formation process in a dynamical model of multidimensional attracting agents. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 11(1), 392–415.
Vancouver
1.
De Smet F, Aeyels D. Clustering conditions and the cluster formation process in a dynamical model of multidimensional attracting agents. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS. 2012;11(1):392–415.
MLA
De Smet, Filip, and Dirk Aeyels. “Clustering Conditions and the Cluster Formation Process in a Dynamical Model of Multidimensional Attracting Agents.” SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 11.1 (2012): 392–415. Print.