Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups

@article{Topaz2004SwarmingPI,
  title={Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups},
  author={Chad M. Topaz and A. Bertozzi},
  journal={SIAM J. Appl. Math.},
  year={2004},
  volume={65},
  pages={152-174}
}
We construct a continuum model for the motion of biological organisms experiencing social interactions and study its pattern-forming behavior. The model takes the form of a conservation law in two spatial dimensions. The social interactions are modeled in the velocity term, which is nonlocal in the population density and includes a parameter that controls the interaction length scale. The dynamics of the resulting partial integrodifferential equation may be uniquely decomposed into… 

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