Biological aggregation driven by social and environmental factors: A nonlocal model and its degenerate Cahn-Hilliard approximation

Autor:	Bernoff, Andrew J., Topaz, Chad M.
Rok vydání:	2015
Předmět:	Nonlinear Sciences - Pattern Formation and Solitons Nonlinear Sciences - Adaptation and Self-Organizing Systems Quantitative Biology - Populations and Evolution
Druh dokumentu:	Working Paper
Popis:	Biological aggregations such as insect swarms and bird flocks may arise from a combination of social interactions and environmental cues. We focus on nonlocal continuum equations, which are often used to model aggregations, and yet which pose significant analytical and computational challenges. Beginning with a particular nonlocal aggregation model [Topaz et al., Bull. Math. Bio., 2006], we derive the minimal well-posed long-wave approximation, which is a degenerate Cahn-Hilliard equation. Energy minimizers of this reduced, local model retain many salient features of those of the nonlocal model, especially for large populations and away from an aggregation's boundaries. Using the Cahn-Hilliard model as a testbed, we investigate the degree to which an external potential modeling food sources can be used to suppress peak population density, which is essential for controlling locust outbreaks. A random distribution of food sources tends to increase peak density above its intrinsic value, while a periodic pattern of food sources can decrease it. Comment: 33 pages, 10 figures; to appear in SIAM J. Appl. Dyn. Sys
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1507.04259 Zobrazit plný text záznamu View this record from Arxiv