Biological Aggregation Driven By Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn-Hilliard Approximation

Authors

Andrew Bernoff, Harvey Mudd CollegeFollow
Chad M. Topaz, Macalester College

Document Type

Article

Department

Mathematics (HMC)

Publication Date

7-15-2015

Abstract

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.

Comments

Preprint: http://arxiv.org/abs/1507.04259

Rights Information

© 2015 Andrew Bernoff, Chad M. Topaz

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Bernoff, Andrew and Topaz, Chad M., "Biological Aggregation Driven By Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn-Hilliard Approximation" (2015). All HMC Faculty Publications and Research. 1075.
https://scholarship.claremont.edu/hmc_fac_pub/1075