dorsal/arxiv
View SchemaA nonlocal continuum model for biological aggregation
| Authors | Chad M. Topaz, Andrea L. Bertozzi, Mark A. Lewis |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0504001 |
| URL | https://arxiv.org/abs/q-bio/0504001 |
Abstract
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.
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"date_created": "2026-03-02T18:01:31.936000Z",
"date_modified": "2026-03-02T18:01:31.936000Z",
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"abstract": "We construct a continuum model for biological aggregations in which\nindividuals experience long-range social attraction and short range dispersal.\nFor the case of one spatial dimension, we study the steady states analytically\nand numerically. There exist strongly nonlinear states with compact support and\nsteep edges that correspond to localized biological aggregations, or clumps.\nThese steady state clumps are approached through a dynamic coarsening process.\nIn the limit of large population size, the clumps approach a constant density\nswarm with abrupt edges. We use energy arguments to understand the nonlinear\nselection of clump solutions, and to predict the internal density in the large\npopulation limit. The energy result holds in higher dimensions as well, and is\ndemonstrated via numerical simulations in two dimensions.",
"arxiv_id": "q-bio/0504001",
"authors": [
"Chad M. Topaz",
"Andrea L. Bertozzi",
"Mark A. Lewis"
],
"categories": [
"q-bio.PE",
"nlin.AO",
"nlin.PS"
],
"title": "A nonlocal continuum model for biological aggregation",
"url": "https://arxiv.org/abs/q-bio/0504001"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "666e3219-31b9-401f-af27-f43337aba201",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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