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Automatic Control, IEEE Transactions on In Automatic Control, IEEE Transactions on, Vol. 52, No. 5. (May 2007), pp. 852-862, doi:10.1109/tac.2007.895842 Key: citeulike:3092459
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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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