TY - JOUR
T1 - Emergent behavior in flocks
AU - Cucker, Felipe
AU - Smale, Steve
PY - 2007/5
Y1 - 2007/5
N2 - We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant β 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 β <1/2 convergence of the flock to a common velocity is guaranteed, while for β ≥ 1/2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only. © 2007 IEEE.
AB - We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant β 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 β <1/2 convergence of the flock to a common velocity is guaranteed, while for β ≥ 1/2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only. © 2007 IEEE.
KW - Consensus reaching problem
KW - Emergence
KW - Flocking
UR - http://www.scopus.com/inward/record.url?scp=34249106048&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-34249106048&origin=recordpage
U2 - 10.1109/TAC.2007.895842
DO - 10.1109/TAC.2007.895842
M3 - RGC 21 - Publication in refereed journal
SN - 0018-9286
VL - 52
SP - 852
EP - 862
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 5
ER -