Graduation Year

2011

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Andrew J. Bernoff

Reader 2

Chad M. Topaz

Terms of Use & License Information

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Rights Information

© 2011 Andrew S. Ronan

Abstract

We study the equilibrium solutions of an integrodifferential equation used to model one-dimensional biological swarms. We assume that the motion of the swarm is governed by pairwise interactions, or a convolution in the continuous setting, and derive a continuous model from conservation laws. The steady-state solution found for the model is compactly supported and is shown to be an attractive equilibrium solution via linear perturbation theory. Numerical simulations support that the steady-state solution is attractive for all initial swarm distributions. Some initial results for the model in higher dimensions are also presented.