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Period-Doubling and Naimark–Sacker Bifurcations of Certain Second Order Quadratic Fractional Difference Equations

We investigate the period-doubling and Naimark–Sacker bifurcations of the equilibrium of the difference equation xn+1 = γxn−1 + δxn Cxn−1 + xn where the parameters γ, δ, C are positive numbers and the initial conditions x−1 and x0 are arbitrary nonnegative numbers such that x−1 + x0 > 0. AMS Subject Classifications: 39A10, 39A20, 39A60, 37B25.

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