Qualitative study of a higher order rational difference equation

Abstract

In this paper we study the behavior of the difference equation xn+1 = αxnx n−l βxn−m + γx n−l , n = 0, 1, ..., where the initial conditions x−r, x−r+1, ..., x0 are arbitrary non zero real numbers where r = max{l, m} is a non-negative integer and α, β and γ are constants. Also, we obtain the solutions of some special cases of this equation. At the end we present some numerical examples to support our theoretical discussion.

On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation

“…Khaliq and Elsayed [7] studied the behavior and obtained some special cases of the difference equation:…”