Local Dynamics and Global Stability of Certain Second-Order Rational Difference Equation with Quadratic Terms

Abstract

We present a complete local dynamics and investigate the global dynamics of the following second-order difference equation: x n + 1 = A x n 2 + E x n - 1 + F / a x n 2 + e x n - 1 + f, n = 0,1, 2,., where the parameters A, E, F, a, e, and f are nonnegative numbers with condition A + E + F > 0, a + e + f > 0, and the initial conditions x - 1, x 0 are arbitrary nonnegative numbers such that a x n 2 + e x n - 1 + f > 0, n = 0,1, 2,.