Synchronization of weakly nonlinear oscillators with Huygens' coupling

Abstract

In this paper, the occurrence of synchronization in pairs of weakly nonlinear self-sustained 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 Poincaré 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.