
   @article{article_843626, title={Dynamics and Bifurcation of $x_{n+1}=\frac{\alpha+\beta x_{n-2 }{A+Bx_{n}+C x_{n-2 }$}, journal={Journal of Mathematical Sciences and Modelling}, volume={4}, pages={25–37}, year={2021}, DOI={10.33187/jmsm.843626}, author={Raddad, Batool and Saleh, Mohammad}, keywords={Fixed points, Stability, Bifurcation}, abstract={&amp;lt;div style="text-align:justify;"&amp;gt; &amp;lt;span style="font-size:14px;"&amp;gt;In this paper, we study dynamics and bifurcation of the third order rational difference equation \begin{eqnarray*} x_{n+1}=\frac{\alpha+\beta x_{n-2 }{A+Bx_{n}+Cx_{n-2 }, ~~n=0, 1, 2, \ldots \end{eqnarray*} with positive parameters $\alpha, \beta, A, B, C$ and non-negative initial conditions $\{x_{-k}, x_{-k+1}, \ldots, x_{0}\}$. We study the dynamic behavior, the sufficient conditions for the existence of the Neimark-Sacker bifurcation, and the direction of the Neimark-Sacker bifurcation. Then, we give numerical examples with figures to support our results. &amp;lt;/span&amp;gt; &amp;lt;/div&amp;gt;}, number={1}, publisher={Mahmut AKYİĞİT}
