  The phenomenon of phase synchronization was evidenced in the 17th century by
Huygens while observing two pendulums of clocks leaning against the same wall.
This phenomenon has more recently appeared as a widespread phenomenon in
nature, and turns out to have multiple industrial applications. The exact
parameter values of the system for which the phenomenon manifests itself are
however delicate to obtain in general, and it is interesting to find formal
sufficient conditions to guarantee phase synchronization. Using the notion of
reachability, we give here such a formal method. More precisely, our method
selects a portion $S$ of the state space, and shows that any solution starting
at $S$ returns to $S$ within a fixed number of periods $k$. Besides, our method
shows that the components of the solution are then (almost) in phase. We
explain how the method applies on the Brusselator reaction-diffusion and the
biped walker examples.
