Asymptotic Dynamics of Attractive-Repulsive Swarms

@article{Leverentz2009AsymptoticDO,
  title={Asymptotic Dynamics of Attractive-Repulsive Swarms},
  author={Andrew J. Leverentz and Chad M. Topaz and Andrew J. Bernoff},
  journal={SIAM J. Appl. Dyn. Syst.},
  year={2009},
  volume={8},
  pages={880-908}
}
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel's first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady state. For the spreading case, the… Expand
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