We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant beta capturing the rate of decay-which in our model is polynomial-of the influence between birds in the flock as they separate in space. Our main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only
%0 Journal Article
%1 Cucker.Smale2007EmergentBehaviorin
%A Cucker, F.
%A Smale, S.
%D 2007
%J Automatic Control, IEEE Transactions on
%K discretetimesystems convergence polynomialsconsensusreachingproblem polynomials discretesystems continuoustimesystems
%N 5
%P 852-862
%R 10.1109/TAC.2007.895842
%T Emergent Behavior in Flocks
%V 52
%X We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant beta capturing the rate of decay-which in our model is polynomial-of the influence between birds in the flock as they separate in space. Our main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only
@article{Cucker.Smale2007EmergentBehaviorin,
abstract = {We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant beta capturing the rate of decay-which in our model is polynomial-of the influence between birds in the flock as they separate in space. Our main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only},
added-at = {2009-09-18T15:57:08.000+0200},
author = {Cucker, F. and Smale, S.},
biburl = {https://www.bibsonomy.org/bibtex/2ce40b374e74c281f6156f78a205bf9ef/janlo},
doi = {10.1109/TAC.2007.895842},
interhash = {799cf4f657958779214e8ce1737abe66},
intrahash = {ce40b374e74c281f6156f78a205bf9ef},
issn = {0018-9286},
jlprojects = {consensus_algorithms},
journal = {Automatic Control, IEEE Transactions on},
keywords = {discretetimesystems convergence polynomialsconsensusreachingproblem polynomials discretesystems continuoustimesystems},
month = May ,
number = 5,
pages = {852-862},
timestamp = {2009-09-18T15:57:08.000+0200},
title = {Emergent Behavior in Flocks},
volume = 52,
year = 2007
}