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On the Invariant Manifolds of the Fixed Point of a Second-Order Nonlinear Difference Equation
(Springer/plenum Publishers, 2020) Turan, Mehmet
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 equationx(n+ 1)=alpha+beta x(n- 1)+x(n- 1)/x(n), where alpha> 0,0 <=beta<1$0\leqslant \beta and the initial conditionsx(- 1)andx(0)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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