Ordinary Differential Equations and Applied Dynamics Commons^™

Optimal Theory Applied In Integrodifference Equation Models And In A Cholera Differential Equation Model, Peng Zhong

Doctoral Dissertations

Integrodifference equations are discrete in time and continuous in space, and are used to model the spread of populations that are growing in discrete generations, or at discrete times, and dispersing spatially. We investigate optimal harvesting strategies, in order to maximize the profit and minimize the cost of harvesting. Theoretical results on the existence, uniqueness and characterization, as well as numerical results of optimized harvesting rates are obtained. The order of how the three events, growth, dispersal and harvesting, are arranged also affects the harvesting behavior.

Cholera remains a public health threat in many parts of the world and improved …

Analytic And Numerical Studies Of A Simple Model Of Attractive-Repulsive Swarms, Andrew S. Ronan

HMC Senior Theses

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.