(untitled) (Contemporary Mathematics, 2025)
This study investigates higher-order recurrence relations by examining the behavior of their solutions through Lie symmetry analysis, periodicity, and stability. Using Lie symmetry techniques, the work in this paper uncovers invariant transformations and structural properties of the equations. The analysis also identifies conditions under which solutions display periodic behavior and evaluates the stability of equilibrium points. To support the theoretical results, graphical representations of the solutions are presented, illustrating the predicted dynamics. These findings offer valuable insights into the qualitative behavior of complex difference equations and considerably extend some existing findings in the literature.