clocks is several orders of magnitude lower than the periods.

6.  The interaction is symmetric, the coupling has the same, very small, constant $\alpha$ when the clock $1$ acts on clock $2$, and conversely.

We compute at this point the phase difference when clock $1$ returns to the initial position. The secular repetition of perturbations leads the system with the two clocks in phase opposition as Huygens observed in 1665 [@Huy]. The discrete dynamical model that we deduce from [@OlMe] for the phase difference between the two clocks $\phi_{n}=\psi_{n}-\varphi_{n}$ is the Adler equation [@adler1946study; @Pit]$$\phi_{n+1}=\phi_{n}+\varepsilon\sin\phi_{n}, \label{Perturb}%$$ with a very small constant $\varepsilon=\frac{16\mu\alpha}{h^{2}}$. In the interval $\left[  0,2\pi\right[  $, there are two fixed points which are $\pi$ and $0$ respectively attracting and reppeling.

Equation (\[Perturb\]) is the starting point from where we begin, in the present paper, the study the three symmetric clocks in mutual interaction.

In any model with a perturbation of phase given by equation (\[Perturb\]) per cycle, i.e., Adler’s perturbation [@adler1946study; @Pit], despite being a physical clock (with Andronov model or any different model) or other type of oscillator, electric, quantic, electronic or biological, the theory presented here for three oscillators interacting by small impacts will be exactly 