Emergent Behavior in Flocks

  title={Emergent Behavior in Flocks},
  author={Felipe Cucker and Stephen Smale},
  journal={IEEE Transactions on Automatic Control},
  • F. CuckerS. Smale
  • Published 15 May 2007
  • Mathematics
  • IEEE Transactions on Automatic Control
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… 

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