\[work3\][The pendulums of clocks ]{}$O_{1},$ $O_{2}$ and $O_{3}$ [have respectively natural angular frequencies ${\omega}_{1}={\omega}%
    _{2}={\omega}_{3}=1$.]{}

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

4.  [The friction coefficient is the same for all the three clocks, ${\mu
    }_{1}={\mu}_{2}={\mu}_{3}={\mu}$. The energy dissipated at each cycle of the three clocks is the same, and the energy furnished by the escape mechanism to compensate the loss of energy to friction in each cycle is $h_{1}=h_{2}%
    =h_{3}=h$. ]{}

5.  [The perturbative interaction is instantaneous. This is a reasonable assumption, since in general the perturbation propagation time between two clocks is several orders of magnitude lower than the periods [@OlMe].]{}

6.  \[hyp6\][The interaction is symmetric. The couplings have the same constant $\alpha$ when one clock acts on another and conversely. In this model $\alpha$ is assumed to be very small.]{}

7.  \[hyp67\][Each perturbation from clock $i$ to clock $j$ (where $i,j\in\{1,2,3\}$ with $i\not =j$), when clock $i$ suffers its internal impact of kinetic energy $h^{2}$, gives rise to a small perturbative change of phase which is in first order a $2\pi$-periodic differentiable odd function $P$ of the real variable $\phi$$$P\left(  \phi\right)  =\varepsilon\sin\phi\text{,} \label{Perturb1}%$$ where 