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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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Cucker et al. (Tue,) studied this question.
www.synapsesocial.com/papers/69dd000ed111c0385b359b1b — DOI: https://doi.org/10.1109/tac.2007.895842
Felipe Cucker
Steve Smale
IEEE Transactions on Automatic Control
City University of Hong Kong
Toyota Technological Institute at Chicago
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