[@gu1975; @Nakao]. When each clock suffers a perturbation, its state can go slightly off the limit cycle and generically jump to another isochron. Moreover, we assume that the limit cycles are structurally stable under small perturbations.

When we consider two oscillators, $1$ and $2$, with orbits on the limit-cycle or sufficiently near the limit cycle, each one has a particular phase, respectively $\varphi$ and $\psi$.

The study of the synchronisation of these two oscillators consists in establishing a dynamical system for the phase difference of the two oscillators.

We have two possible lines of research [@Pit]. The first is to consider the phase difference along continuous time, i.e., to look at the function $\phi\left(  t\right)  =\psi\left(  t\right)  -\varphi\left(  t\right)  $ for $t\in\left[  0,+\infty\right[  $. The second line of research, that we adopt in this paper, is to consider the phase difference $\phi_{n}=\psi_{n}%
-\varphi_{n}$ taken at discrete instants $n=0,1,2,\ldots$. In this paper, we consider exclusively this last approach.

There is phase synchronisation when the phase differences between the oscillators tend to a specific attractor. When this attractor is an isolated point, then there is phase locking. Naturally, richer coupled states can occur [@Martens]. The main goal for any theory of synchronisation 