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Emergent Behavior in Flocks

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2 Author(s)
Cucker, F. ; Dept. of Math., City Univ. of Hong Kong ; Smale, S.

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

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Automatic Control, IEEE Transactions on  (Volume:52 ,  Issue: 5 )