On a class of second-order nonlinear difference equation

Abstract

Abstract In this paper, we consider the rule of trajectory structure for a kind of second-order rational difference equation. With the change of the initial values, we find the successive lengths of positive and negative semicycles for oscillatory solutions of this equation, and the positive equilibrium point 1 of this equation is proved to be globally asymptotically stable. Mathematics Subject Classification (2000) 39A10

Keywords

• rational difference equation
• trajectory structure rule
• semicycle length; periodicity
• global asymptotic stability