GLOBAL DYNAMICAL BEHAVIOURS AND PERIODICITY OF A CERTAIN QUADRATIC-RATIONAL DIFFERENCE EQUATION WITH DELAY

摘要

Our aim in this paper is to deal with the dynamics of following higher order difference equation x(n+ 1) = A+ B x(n- m)/x(n)(2) where A, B > 0, and initial values are positive, and m = {1,2,...}. Furthermore, we discuss the periodicity, boundedness, semi-cycles, global asymptotic stability of solutions of these equations. We also handle the rate of convergence of solutions of these difference equations.