Qualitative properties for a fourth-order rational difference equation

Abstract: In this paper, we use a method different from the known literature to investigate the qualitative properties of the following fourth-order rational difference equation: where and the initial values . The successive lengths of positive and negative semicycles of nontrivial solutions of the above equation is found to periodically occur, that is, , or, . By using the rule, the positive equilibrium point of the equation is verified to be globally asymptotically stable. [Copyright &y& Elsevier]