On a \((2,2)\)-rational recursive sequence (Q2495060)

The authors investigate the asymptotic behavior of the solutions of the second-order rational difference equation \[ y_{n+1}=\frac{\alpha+\beta y_n}{1+y_{n-1}};\quad n=0,1,2,\dots, \] where \(x_{-1},x_0\geq 0\), \(\alpha<0\) and \(\beta\in \mathbb{R}\). In particular, they establish the boundedness of solutions and the global asymptotic stability of the equilibrium solution(s) for different ranges of the parameters \(\alpha\) and \(\beta\).