Date of Award
5-2011
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
First Thesis Advisor
Andrew J. Bernoff
Second Thesis Advisor
Chad M. Topaz
Rights Information
© 2011 Andrew S. Ronan
Terms of Use & License Information
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
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.
Recommended Citation
Ronan, Andrew S., "Analytic and Numerical Studies of a Simple Model of Attractive-Repulsive Swarms" (2011). HMC Senior Theses. Paper 11.
http://scholarship.claremont.edu/hmc_theses/11