%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 }