Date of Award
Doctor of Philosophy (PhD)
We investigate t he boundedness character, the periodic nature, and the stability behavior of solutions of three difference equations.
The first equation is
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.
Al-Amleh, Amal M., "Boundedness, Periodicity and Stability of Some Difference Equations" (1998). Open Access Dissertations. Paper 544.