  The cutoff phenomena for Markovian dynamics have been observed and rigorously
verified for a multitude of models, particularly for Glauber-type dynamics on
spin systems. However, prior studies have barely considered irreversible
chains. In this work, the cutoff phenomenon of certain cyclic dynamics are
studied on the hypercube $\Sigma_{n} = Q^{V_{n}}$, where $Q = \{1, 2, 3\}$ and
$V_{n} = \{1,...,n\}$. The main feature of these dynamics is the fact that they
are represented by an irreversible Markov chain. Based on the coupling
modifications suggested in a previous study of the cutoff phenomenon for the
Curie-Weiss-Potts model, a comprehensive proof is presented.
