Title :
Emergent Behavior in Flocks
Author :
Cucker, Felipe ; Smale, Steve
Author_Institution :
Dept. of Math., City Univ. of Hong Kong
fDate :
5/1/2007 12:00:00 AM
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
Keywords :
continuous time systems; discrete systems; polynomials; consensus reaching problem; continuous time systems; convergence; discrete time systems; polynomials; Birds; Computer simulation; Convergence; Councils; Gravity; H infinity control; Marine animals; Mathematics; Polynomials; Consensus reaching problem; emergence; flocking;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2007.895842
