Award Date

5-1-2012

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

David G. Costa

Second Committee Member

Hossein Tehrani

Third Committee Member

Zhonghai Ding

Fourth Committee Member

Paul Schulte

Number of Pages

38

Abstract

It was recently shown that the nonlinear logistic type ODE with periodic harvesting has a bifurcation on the periodic solutions with respect to the parameter ε:

u' = f (u) - ε h (t).

Namely, there exists an ε0 such that for 0 < ε < ε0 there are two periodic solutions, for ε = ε0 there is one periodic solution, and for ε >ε0 there are no periodic solutions, provided that....

In this paper we look at some numerical evidence regarding the behavior of this threshold for various types of harvesting terms, in particular we find evidence in the negative or a conjecture regarding the behavior of this threshold value.

Additionally, we look at analagous steady states for the reaction-diusion IBVP with logistic growth and positive harvesting: Using phase plane arguments we show that there is a threshold value of such that this BVP has no positive solutions.

Keywords

Differential equations; Harvesting; Logistic; Periodic

Disciplines

Mathematics | Ordinary Differential Equations and Applied Dynamics

Language

English


Share

COinS