Open-loop synchronization: uncoupled oscillators may show synchronized motion*

In this paper, synchronous behaviour is induced in a group of identical dynamical oscillators by applying a synchronizing signal, which is generated by an exogenous system. Specifically, a second order dynamical system driven by a pulse train is designed. The output of this system is further applied to a group of identical oscillatory systems, forcing them to synchronize. The novelty in this approach is that the synchronizing signal does not require any information from the dynamics of the systems to synchronize, i.e. the systems are uncoupled and they synchronize not because of an interaction between them but because of the influence of the synchronizing exogenous signal. In the analysis, the proposed synchronizing signal is applied to a set of chaotic systems, to a set of biological systems, and to a set of mechanical oscillators.