Dynamic behavior of a second-order nonlinear rational difference equation

Abstract

This paper deals with the global attractivity of positive solutions of the second-order nonlinear difference equation xn+1 = axk n + b k∑−1 j=1 x j nx k−j n−1 + cx k n−1 Axk n + B k∑−1 j=1 x j nx k−j n−1 + Cxk n−1 , k = 3, 4, ..., n = 0, 1, ..., where the parameters a, b , c , A, B , C and the initial values x0 , x−1 are arbitrary positive real numbers