Global asymptotic stability for a nonlinear delay difference equation

AbstractIn this paper, a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, $$x_{n + 1} = \frac{{x_n + x_{n---1} x_{n---2 } + a}}{{x_n x_{n---1} + x_{n---2} + a}}, n = 0,1,...,$$ where aε [0,∞] and the initial values x−2,x−1,x0ε (0,∞). As a special case, a conjecture by Ladas is confirmed.