Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference Equations - Raafat Abo-Zeid; Abdul Qadeer Khan (Discrete Dynamics in Nature and Society, 2021)
In this work, we derive the solution formulas and study their behaviors for the difference equations xn+1=αxnxn−3/−βxn−3+γxn−2,n∈ℕ0 and xn+1=αxnxn−3/βxn−3−γxn−2,n∈ℕ0 with real initials and positive parameters. We show that there exist periodic solutions for the second equation under certain conditions when β2<4αγ. Finally, we give some illustrative examples.