On the dynamics of a higher order rational difference equations

The main objective of this paper is to study the global stability of the positive solutions and the periodic character of the difference equation yn+1=ayn+byn−t+cyn−l+dyn−k+eyn−sαyn−k+βyn−s,n=0,1,…,with positive parameters and non-negative initial conditions. Numerical examples to the difference equation are given to explain our results.