Global dynamics and bifurcations of two quadratic fractional second order difference equations (Q2792490)

The paper is devoted to the following two difference equations NEWLINE\[NEWLINE x_{n+1}=\frac{\beta x_nx_{n-1}+\gamma x_{n-1}}{Ax^2_n+Bx_nx_{n-1}},\quad n=0,1,\dots NEWLINE\]NEWLINE and NEWLINE\[NEWLINE x_{n+1}=\frac{\alpha x^2_n+\beta x_nx_{n-1}+\gamma x_{n-1}}{Ax^2_n},\quad n=0,1,\dots NEWLINE\]NEWLINE where the parameters \(\alpha\), \(\beta\), \(\gamma\), \(A\), \(B\) and the initial values \(x_{-1}\), \(x_0\) are positive numbers.NEWLINENEWLINEThe authors use the theory of monotone maps developed in works by \textit{M. Garić-Demirović} et al. [Discrete Dyn. Nat. Soc. 2009, Article ID 153058, 34 p. (2009, Zbl 1177.37046)] and by \textit{M. R. S. Kulenović} and \textit{O. Merino} [Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 8, 2471--2486 (2010, Zbl 1202.37027)] to describe precisely the basins of attraction of all attractors of the above equations and bifurcations.