Synchronization of weakly nonlinear oscillators with Huygens' coupling

In this paper, the occurrence of synchronization in pairs of weakly nonlinear selfsustained oscillators that interact via Huygens’ coupling, i.e. a suspended rigid bar, is treated. In the analysis, a generalized version of the classical Huygens’ experiment of synchronization of two coupled pendulum clocks is considered, in which the clocks are replaced by arbitrary self-sustained oscillators. Sufficient conditions for the existence and stability of synchronous solutions in the coupled system are derived by using the Poincar´e method. The obtained results are supported by computer simulations and experiments conducted on a dedicated experimental platform. It is demonstrated that the mass of the coupling bar is an important parameter with respect to the limit synchronous behaviour in the oscillators