On the critical exponent for flocks under hierarchical leadership

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

  • Felipe Cucker
  • Jiu-Gang Dong

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)1391-1404
Journal / PublicationMathematical Models and Methods in Applied Sciences
Volume19
Issue numberSUPPL. 1
Publication statusPublished - Aug 2009

Abstract

Very recently, a model for flocking was introduced by Cucker and Smale together with a proof of convergence. This proof established unconditional convergence to a common velocity provided the interaction between agents was strong enough and conditional convergence otherwise. The strength of the interaction is measured by a parameter β <0 and the critical value at which unconditional convergence stops holding is β = 1/2. This model was extended by Shen to allow for a hierarchical leadership structure among the agents and similar convergence results were proved. But, for discrete time, unconditional convergence was proved only for $\beta <\frac{1}{2k}$ (k being the number of agents). In this note we improve on this result showing that unconditional convergence holds indeed for β <1/2. © 2009 World Scientific Publishing Company.

Research Area(s)

  • Hierarchical leadership, Unconditional convergence.

Citation Format(s)

On the critical exponent for flocks under hierarchical leadership. / Cucker, Felipe; Dong, Jiu-Gang.
In: Mathematical Models and Methods in Applied Sciences, Vol. 19, No. SUPPL. 1, 08.2009, p. 1391-1404.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review