On the difference equation \(x_{n+1}=\frac{\alpha x_{n-1}+\beta x_{n-k}}{Ax_{n-1}+Bx_{n-k}}\)
The solutions of the difference equation in the title with positive coefficients and positive initial values are studied with respect to persistence and 2-periodicity. Moreover, conditions are given such that the equilibrium is locally asymptotically stable resp. a global attractor.
scientific article; zbMATH DE number 5354281