Andrew S. Ronan

Picture of Andrew S. Ronan.

Thesis

Analytic and Numerical Studies of a Simple Model of Attractive-Repulsive Swarms

Advisor
Andrew Bernoff
Second Reader(s)
Chad M. Topaz (Macalester College)

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.

Proposal

Dynamics of Attractive–Repulsive Swarms

Additional Materials

Poster