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1. 2. 2016.
Local Dynamics and Global Stability of Certain Second‐Order Rational Difference Equation with Quadratic Terms
We present a complete local dynamics and investigate the global dynamics of the following second‐order difference equation: xn+1=Axn2+Exn-1+F/axn2+exn-1+f, n=0,12,,… , 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, x0 are arbitrary nonnegative numbers such that axn2+exn-1+f>00,12, n=,,….