Abstract
This paper addresses the asymptotic approximations of the stable and unstable manifolds for the saddle fixed point and the 2-periodic solutions of the difference equation xn+ 1 = α + βxn− 1 + xn− 1/xn, where α > 0, \(0\leqslant \beta <1\) and the initial conditions x− 1 and x0 are positive numbers. These manifolds determine completely global dynamics of this equation. The theoretical results are supported by some numerical examples.
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The authors would like to extend their immense gratitude to the anonymous referees, whose valuable comments helped to improve the manuscript essentially.
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Turan, M. On the Invariant Manifolds of the Fixed Point of a Second-Order Nonlinear Difference Equation. J Dyn Control Syst 26, 673–684 (2020). https://doi.org/10.1007/s10883-019-09472-3
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DOI: https://doi.org/10.1007/s10883-019-09472-3