الفهرس 
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Abstract
The aim of this work is to study the qualitative behavior of the solutions of some nonlinear difference equations of different orders. The thesis consists of four chapters as follows: Chapter 1. This chapter is an introductory chapter that contains some basic definitions and elementary results that will be used throughout the next chapters. Chapter 2. We study the global attractor by using full limiting sequences, the rate of convergence, the permanence, the periodicity and the rate of convergence of solutions of the rational difference equation. Chapter 3. In this chapter, we study the local stability, the permanence, the semicycles, the rate of convergence, the periodicity character, and local stability analysis of the period two solutions of the rational difference equation. Chapter 4.This chapter is an investigated the local stability, the boundedness, the globally asymptotically stable, the global attractor by the method of the full limiting sequences, the rate of convergence and the periodicity character of solutions of a non Autonomous difference equation.
Key words: Difference equation, stability, oscillation, boundedness, global stability, rate of convergence, Periodicity and local stability analysis of the period two.