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University of St. Thomas Center for Applied Mathematics

Biological swarms and their mathematical models

Speaker: Chad Topaz
Affiliation: Macalester
Presentation Date: November 18, 2009

Abstract:
Biological aggregations such as insect swarms, bird flocks, and fish schools are arguably some of the most common and least understood patterns in nature. These groups are thought to arise chiefly from "social forces" acting on individual organisms, such as attraction (for protection and mate choice) and repulsion (for collision avoidance). In this talk, I will introduce biological swarms and describe a mathematical modeling approach. I will also present research on locust swarms performed with two undergraduate research students. The mathematical model is a high-dimensional system of ordinary differential equations incorporating gravity, wind, and social interactions. In certain parameter regimes, the model has emergent "rolling" solutions morphologically similar to locust swarms observed by biologists.