Open Access Senior Thesis
Bachelor of Science
Andrew J. Bernoff
Chad M. Topaz
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
© 2011 Andrew S. Ronan
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.
Ronan, Andrew S., "Analytic and Numerical Studies of a Simple Model of Attractive-Repulsive Swarms" (2011). HMC Senior Theses. 11.