is to obtain this phase difference dynamics and to establish the existence and nature of the attractor. In the case of Huygens observations, the attractor was the point $0$ or the point $\pi$ and the phase dynamics was unidimensional.

The Andronov model for an isolated clock
----------------------------------------

We recall here the model for the sake of completeness of this article. Assuming that dry friction predominates in the internal metal pieces of the clock and the viscous damping is not predominant, using the angular coordinate $q$, the differential equation governing the isolated pendulum clock is$$\ddot{q}+\mu\text{ }\operatorname*{sign}\dot{q}+q=0,$$ where $\mu>0$ is the dry friction coefficient and $\operatorname*{sign}\left(
x\right)  $ is the classical function taking the value $-1$ at $x<0$ and $1$ at $x>0$. In [@And] it was considered that, in each cycle, the escape mechanism gives to the pendulum a fixed amount of normalized kinetic energy $\frac{h^{2}}{2}$ so to compensate the loss of kinetic energy occurred because of the dry friction in each complete cycle. This transfer of kinetic energy is called a *kick*. The origin is fixed so that the kick is given precisely when $q=-\mu$. The phase portrait is shown in Fig. $1$.

\[h\]

[limitcycle.eps]{}

As in [@OlMe], with initial conditions 