Behavior of solutions of higher-order difference equations

This paper examined a new class of difference equations, focusing on the stability, boundedness, and periodicity of solutions. Special cases admitting explicit solutions wrere also considered. Numerical examples were provided to confirm the theoretical results and illustrate the consistency between analytical predictions and computational observations. These findings contributed to a deeper understanding of the qualitative behavior of discrete-time dynamical systems and offered insight into the dynamics of higher-order difference equations.