In this work, we provide a detailed study on the behavior of solutions of a $k$-dimensional system of rational difference equations, extending some existing results in the literature. We use the linearized stability theory to establish conditions for the local stability of the corresponding unique equilibrium point, and to show its global stability, we prove that the equilibrium point is a global attractor. Also, conditions for the existence of periodic solutions are provided. Our obtained results are confirmed by some examples.

This paper employed the well-known Riccati transformation method to deduce a Kneser-type oscillation criterion for second-order dynamic equations. These results are considered an extension and improvement of the known Kneser results for second-order differential equations and are new for other time scales. We have included examples to highlight the significance of the results we achieved.