A Nonlocal Continuum Model for Biological Aggregation

@article{Topaz2005ANC,
  title={A Nonlocal Continuum Model for Biological Aggregation},
  author={Chad M. Topaz and A. Bertozzi and Mark A. Lewis},
  journal={Bulletin of Mathematical Biology},
  year={2005},
  volume={68},
  pages={1601-1623}
}
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short-range dispersal. For the case of one spatial dimension, we study the steady states analytically and numerically. There exist strongly nonlinear states with compact support and steep edges that correspond to localized biological aggregations, or clumps. These steady-state clumps are reached through a dynamic coarsening process. In the limit of large population size… 

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