Global dynamics of a higher order difference equation with a quadratic term

Abstract

In this paper, we investigate the dynamics of the following higher order difference equation x(n+1) = A + B x(n)/x(n-m)(2) with A, B and initial conditions are positive numbers, and m is an element of {2, 3, ...}. Especially we study the boundedness, periodicity, semi-cycles, global asymptotically stability and rate of convergence of solutions of related higher order difference equations.