# 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}
}
• Published 1 January 2004
• Physics
• SIAM J. Appl. Math.
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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