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Permanent link (DOI): https://doi.org/10.7939/R3TJ8V

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A nonlocal continuum model for biological aggregation. Open Access

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Author or creator
Topaz, C. M.
Bertozzi, A. L.
Lewis, M. A.
Additional contributors
Subject/Keyword
integrodifferential equation
pattern
swarm
aggregation
Type of item
Journal Article (Published)
Language
English
Place
Time
Description
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 approached through a dynamic coarsening process. In the limit of large population size, the clumps approach a constant density swarm with abrupt edges. We use energy arguments to understand the nonlinear selection of clump solutions, and to predict the internal density in the large population limit. The energy result holds in higher dimensions as well, and is demonstrated via numerical simulations in two dimensions.
Date created
2006
DOI
doi:10.7939/R3TJ8V
License information
Rights
© 2006 Springer. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.
Citation for previous publication
Topaz, C. M., Bertozzi, A. L., & Lewis, M. A. (2006). A nonlocal continuum model for biological aggregation. Bulletin of Mathematical Biology, 68(7), 1601-1623.
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