On the dynamics of a higher order rational difference equations

Abstract

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−s
αyn−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.