form, stability and behavior of the solutions of a variety of systems of differences equations

Abstract

Our objective in this thesis is to study the qualitative behavior and the solvability of some systems of difference equations. In the first two chapters, we will study a nonautonomous fourth-order system of difference equations and a general second order system defined byhomogeneous functions. More precisely, we will discuss stability of equilibrium points, periodicity and oscillatory behavior and we will support and confirm our results with some examples and applications. In the last chapter, we will establish explicit formulas of well-defined solutions for a two dimensional system of nonlinear difference equations in terms of a generalized Fibonacci sequence, as well as the formulas of the well-defined solutions of its corresponding three-dimensional case and some more general systems.