Existence, stability, boundedness, and periodicity of some difference equations

We investigate the asymptotic behavior, the oscillatory character and the periodic nature of solutions of the difference equation [special characters omitted]where A is a real parameter and the initial conditions are arbitrary nonzero real numbers. We also give a detailed description of the set of initial conditions [special characters omitted] for which the system of difference equations with real parameters a, b, c, and d [special characters omitted]is well defined for all n ≥ 0. We then present an analysis of the short term and long term behavior of its solutions. Finally we investigate the periodic character and the global stability of solutions of [special characters omitted]with positive parameters and positive initial conditions