Global asymptotic stability in a rational recursive sequence

摘要

In this paper, we study the global stability of the difference equationxn=a+bxn−1+cxn−12d−xn−2,n=1,2,…,where a, b⩾0 and c, d>0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive solution of the equation in the basin exponentially converges to the attractor.