Global Behavior of Two Rational Third Order Difference Equations

In this paper, we solve and study the global behavior of all admissible solutions of the two difference equations xₙ₊₁=xₙxₙ₋₂xₙ₋₁-xₙ₋₂, n=0,1,..., and xₙ₊₁=xₙxₙ₋₂-xₙ₋₁+xₙ₋₂, n=0,1,..., where the initial values x₋₂, x₋₁, x₀ are real numbers.\\ We show that every admissible solution for the first equation converges to zero. For the other equation, we show that every admissible solution is periodic with prime period six. Finally we give some illustrative examples.