### Naimark-Sacker bifurcation of a certain second order quadratic fractional difference equation

#### Abstract

We investigate the Naimark-Sacker Bifurcation of the equilibrium of some special cases of the difference equation $x_{n+1}=\frac{\beta x_n x_{n-1}+ \gamma x_{n-1}^2 +\delta x_n}{ B x_n x_{n-1}+C x_{n-1}^2 +D x_n}$ where the parameters $\beta, \gamma,\delta, B, C, D$ are nonnegative numbers which satisfy $B+C+D>0$ and the initial conditions $x_{-1}$ and $x_0$ are arbitrary nonnegative numbers such that $B x_n x_{n-1}+C x_{n-1}^2 +D x_n >0$ for all $n \geq 0$.

**How to Cite this Article:**M.R.S. Kulenovic, E. Pilav, E. Silic, Naimark-Sacker bifurcation of a certain second order quadratic fractional difference equation, J. Math. Comput. Sci., 4 (2014), 1025-1043 Copyright © 2014 M.R.S. Kulenovic, E. Pilav, E. Silic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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