On the dynamics of a higher order rational difference equations

http://dx.doi.org/10.1016/j.joems.2016.06.010

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.