Boundedness, Periodicity and Stability of Some Difference Equations

Author

Amal M. Al-Amleh, University of Rhode Island

Date of Award

1998

Degree Type

Dissertation

Degree Name

Doctor of Philosophy in Applied Mathematical Sciences

Specialization

Applied Mathematics

Department

Mathematics

First Advisor

Gerry Ladas

Abstract

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

The first equation is

[Mathematical equations can not be displayed here, refer to PDF]

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 the period in terms of A, B, and the initial conditions.

The second equation is

[Mathematical equations can not be displayed here, refer to PDF]

where the function ∫ satisfies the strong negative feedback property.

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

[Mathematical equations can not be displayed here, refer to PDF]

where α ∈ (1,∞), B ∈ (0,∞), and γ ∈ (0, 1) and the initial conditions x₀ and y₀ are arbitrary positive numbers.

Recommended Citation

Al-Amleh, Amal M., "Boundedness, Periodicity and Stability of Some Difference Equations" (1998). Open Access Dissertations. Paper 544.
https://digitalcommons.uri.edu/oa_diss/544