Date of Award

1998

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Gerry Ladas

Abstract

We investigate t he boundedness character, the periodic nature, and the stability behavior of solutions of three difference equations.

The first equation is

xn+1=max(A/xn,B/xn-1), n=0,1,...

where the parameters A and B and the initial conditions x-1 and x0 are nonzero real numbers. We obtain necessary and sufficient conditions for every solution to be eventually periodic. We also give a precise description of t he period in terms of A, B, and t he initial conditions.

The second equation is

xn+1 = f(xn,xn-1,...,xn-k),n=0,1,...

where the function f satisfies the strong negative feedback property.

Finally we investigate the boundedness character of the positive solutions of the Plant-Herbivore System

((xn+1=axn/Bxn+eyn)(Yn+1= y(xn+1)Yn)) ,n=0,1,...

where a = (1,∞), B = (0,∞), and y = (0,1) and the initial conditions x0 and y0 are arbitrary positive numbers.

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