for the sake of completeness and to make our three clocks model more simple and natural to deal with.

To describe and investigate the effect of the kicks, we construct a discrete dynamical system for the phase difference between the two clocks. We compute each cycle using as reference one of the clocks (the choice is irrelevant, since the model is symmetric). We choose, to fix ideas, clock 1 as the reference: whenever its phase reaches $0$ $\left(  \operatorname{mod}%
2\pi\right)  $, the number of cycles increases one unit from $n$ to $n+1$.

If there exists an attracting fixed point for that dynamical system, the phase locking occurs. As in [@OlMe], the assumptions are the following.

1.  Dry friction.

2.  The pendulums have the same natural angular frequency $\omega=1$.

3.  The perturbation in the momentum is always in the same vertical direction in the phase space [@Abr2; @Abr].

4.  Since the clocks have the same construction, the energy dissipated at each cycle of the two clocks is the same, $h_{1}=h_{2}=h$. The friction coefficient is the same for both clocks, $\mu_{1}=\mu_{2}=\mu$.

5.  The perturbative interaction is instantaneous. This is a reasonable assumption, since in general the perturbation propagation time between the two 