On Two Nonlinear Difference Equations

The behavior of solutions of the following nonlinear difference equations \[ xₙ₊₁=/p+x_n^ν and yₙ₊₁=/-p+y_n^ν, \] where p, q ⁺ and ν∈ N are studied. The solution form of these two equations when $ν=1$ are expressed in terms of Horadam numbers. Furthermore, the behavior of their solutions are investigated for all integer $ν> 0$ and several numerical examples are presented to illustrate the results exhibited. The present work generalizes those seen in [{ Adv. Differ. Equ.}, { 2013}:174 (2013), 7 pages].