Global attractivity of the difference equation xn+1=α+(xn−k/xn)

摘要

In this paper, we investigate the global stability of all negative solutions of the difference equationxn+1=α+xn−kxn,n=0,1,…,where α<1 is a real number, k⩾1 is an integer, and the initial conditions x−k,…,x0 are arbitrary real numbers. We show that the unique negative equilibrium of the equation is a global attractor with a basin that depends on certain conditions of the coefficient.