Qualitative behavior of a rational difference equation

This article is concerned with the following rational difference equation yn+1 = (yn + yn-1)/(p + ynyn-1) with the initial conditions; y-1, y0 are arbitrary positive real numbers, and p is positive constant. Locally asymptotical stability and global attractivity of the equilibrium point of the equation are investigated, and non-negative solution with prime period two cannot be found. Moreover, simulation is shown to support the results.