Global asymptotic stability in a rational recursive sequence (Q702622)

The global stability of the difference equation \[ x_{n}=\frac{a+bx_{n-1}+cx_{n-1}^2}{d-x_{n-2}}, \quad n=1,2,\dots \] where \(a,b\geq 0\) and \(c,d>0\) is studied. It is shown that one nonnegative equillibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive solution of the equation in the basin exponentially converges to the attractor.