Turan, MehmetMathematics2024-07-052024-07-0520201079-27241573-869810.1007/s10883-019-09472-32-s2.0-85077717907https://doi.org/10.1007/s10883-019-09472-3https://hdl.handle.net/20.500.14411/3250Turan, Mehmet/0000-0002-1718-3902This 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.eninfo:eu-repo/semantics/closedAccessStable manifoldUnstable manifoldCenter manifoldNormal formArticleQ3Q3264673684WOS:0005573903000051