Periodic Solutions of Some Higher Order Rational Difference Equations

In this paper, the periodicity of the solutions of some higher order difference equations w_(n+1)=(w_n w_(n-k-1))/w_(n-k) , n, k ∈ N_0 " " are investigated where the initial conditions are arbitrary real numbers such that the denominator is always nonzero. While investigating the periodicity of this higher order equation, first the special cases of the equation were considered then a generalization was given for the periodicity of the solution of this higher order difference equation. Moreover, some numerical examples are given to illustrate our theoretical results.