On flocks influenced by closest neighbors

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

28 Scopus Citations
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Author(s)

  • Felipe Cucker
  • Jiu-Gang Dong

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)2685-2708
Journal / PublicationMathematical Models and Methods in Applied Sciences
Volume26
Issue number14
Online published16 Dec 2016
Publication statusPublished - 30 Dec 2016

Abstract

We prove, both for continuous time and discrete time, results establishing convergence to flocking in a model in which each agent is influenced by only a few closest neighbors. We show unconditional convergence to flocking when this number of closest neighbors is at least half of the population and, otherwise, conditional convergence. That is, convergence to flocking provided the initial positions and velocities satisfy an explicit constraint. We also show that the proportion of neighbors necessary for unconditional convergence, one-half, is sharp. Nothing less will do.

Research Area(s)

  • flocking, Particle systems

Citation Format(s)

On flocks influenced by closest neighbors. / Cucker, Felipe; Dong, Jiu-Gang.
In: Mathematical Models and Methods in Applied Sciences, Vol. 26, No. 14, 30.12.2016, p. 2685-2708.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review