Dynamics and behavior of a higher order rational recursive sequence

Abstract

In this article we study the global convergence result, boundedness, and periodicity of solutions of the difference equation xn+1 = ax n-s + bxn-l + cxn-k/dxn-l + ex n-k n = 0,1, . . ., where the parameters a, b, c, d and e are positive real numbers and the initial conditions x-t, x -t+1, . . ., x-1 and x0 are positive real numbers where t = max{s, l, k}. © 2012 Elsayed and El-Dessoky;.