Dynamics and Behavior of a Second Order Rational Difference equation E. M. Elsayed 1;2 , M. M. El-Dessoky 1;2 , and Asim Asiri 1 1 King Abdulaziz University, Faculty of Science, Mathematics Department, P. O. Box 80203, Jeddah 21589, Saudi Arabia. 2 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt. E-mail: emelsayed@mans.edu.eg, dessokym@mans.edu.eg, amkasiri@kau.edu.sa ABSTRACT In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the difference equation x n+1 = ax n + b + cx n1 d + ex n1 ; n =0; 1; :::; where the parameters a; b; c; d and e are positive real numbers and the initial conditions x 1 and x 0 are positive real numbers. Keywords: stability, periodic solutions, boundedness, difference equations. Mathematics Subject Classication: 39A10  1 Introduction Difference equations have been used to describe evolution phenomena since most measure- ments of time-evolving variables are discrete. More signicantly, difference equations are used in the study of discretization methods for differential equations. The theory of difference equa- tions has some results that have been acquired approximately as natural discrete analogues of corresponding results of differential equations [35]. The study of rational difference equations of order greater than one is quite ambitious and worthwhile since some paradigms for the development of the basic theory of the global behav- ior of nonlinear difference equations of order greater than one come from the results of rational difference equations. However, there have not been any useful general methods to study the global behavior of rational difference equations of order greater than one so far. Therefore, the study of rational difference equations of order greater than one deserves further consideration. Many research have been done to study the global attractivity, boundedness character, peri- odicity and the solution form of nonlinear difference equations. For example, Agarwal et al. [2] 794 J. COMPUTATIONAL ANALYSIS AND APPLICATIONS, VOL. 16, NO.4, 2014, COPYRIGHT 2014 EUDOXUS PRESS, LLC ELSAYED ET AL 794-807