fire models of Kuramoto [@Campbell1997; @Campbell1999; @Kuramoto1975; @Mirollo1990; @Strogatz2000].

The paper is organised in $5$ sections. In section $2$, we discuss the original model of the pendulum clock and we briefly recall the model for two identical clocks. In section $3$, we deduce the model for three identical clocks hanging at the same wall with mutual interactions. In section$\ 4$, we analyse the model, computing its symmetries and stabilities. In section $5 $, we draw conclusions and point out directions for future work.

Model for the synchronisation of two oscillators
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Some background
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For the sake of completeness we present here a very short theory of synchronisation for two oscillators exchanging small perturbations at each cycle. We consider identical oscillators. This theory can be applied to networks of identical oscillators, electronic oscillators and many other real world systems. We intend to consider, in future work, the case of slighly different oscillators, which give rise to regions of stability versus instability in the parameter space of these systems, i.e., Arnold Tongues [@boyland1986; @gilmore2011].

For basic, classical definitions and notions related to synchronisation, like phase and frequence, we follow and refer to [@Pit], and for concepts concerning general theory of dynamical 