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

Abstract EN

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 , … .