Abstract
Difference equations appear as natural descriptions of observed evolution, phenomena because most measurements of time evolving variables are discrete and as such those equations are in their own right important mathematical models. More importantly, difference equations also appear in the study of discretization methods for differential equations. Several results in the theory of difference equations have been obtained as more or less natural discrete analogues of corresponding results of differential equations. This is especially true in the case of Lyapunov theory of stability. Nonetheless, the theory of difference equations is a lot richer than the corresponding theory of differential equations. For example; a simple difference equation resulting from a first order differential may have a phenomena often called appearance of "ghost" solutions or existence of chaotic orbits that can only happen for higher order differential equations and the theory of difference equations is interesting in itself. The aim of this thesis is to study the qualitative behavior of solution of some nonlinear difference equations of different order. We discussed, in detail the following