Dynamics of a rational multi-parameter second order difference equation with cubic numerator and quadratic monomial denominator

The asymptotic behavior (such as convergence to an equilibrium, convergence to a 2-cycle, and divergence to infinity) of solutions of the following multi-parameter, rational, second order difference equation x_{n+1} =(ax_{n}^3+ bx_{n}^2x_{n-1}+cx_{n}x_{n-1}^2+dx_{n-1}^3)/x_{n}^2, x_{-1},x_{0}\in R, is studied in this paper.