Advanced search
1 file | 366.63 KB Add to list

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

Filip De Smet (UGent) and Dirk Aeyels (UGent)
Author
Organization
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.
Keywords
clustering, self-organization, phase transition, EVOLUTION, EQUATIONS, AGGREGATION, OSCILLATORS, BEHAVIOR, multiagent systems

Downloads

  • SIADS final mdim.pdf
    • full text
    • |
    • open access
    • |
    • PDF
    • |
    • 366.63 KB

Citation

Please use this url to cite or link to this publication:

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.
APA
De Smet, F., & 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.
Chicago author-date
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.
Chicago author-date (all authors)
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.
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.
IEEE
[1]
F. De Smet and D. Aeyels, “Clustering conditions and the cluster formation process in a dynamical model of multidimensional attracting agents,” SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 11, no. 1, pp. 392–415, 2012.
@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},
  keywords     = {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},
}

Altmetric
View in Altmetric
Web of Science
Times cited: