Huygens synchronisation of three clocks equidistant from each other

In this paper we study the synchronisation of three identical oscillators, i.e., clocks, hanging from the same hard support. We consider the case where each clock interacts with the other two clocks. The synchronisation is attained through the exchange of small impacts between each pair of oscillators. The fundamental result of this article is that the final locked state is at phase difference of ((2{\pi})/3) from successive clocks (clockwise or counter-clockwise). Moreover, the locked states attract a set whose closure is the global set of initial conditions. The methodology of our analysis consists in the construction a model, which is a non-linear discrete dynamical system, i.e. a non-linear difference equation. The results are extendable to any set of three oscillators under mutual symmetric interaction, despite the particular models of the oscillators