Emergent Behavior in Flocks
Felipe CuckerDepartment of Mathematics, City University of Hong Kong, Hong Kong, ChinaSteve SmaleToyota Technological Institute at Chicago, University of Chicago, Chicago, IL, USA
2007en
ABI
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
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Cited by 30 references