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
