Synchronization of Chaotic Systems with Huygens-Like Coupling

In this paper, we consider the synchronization of chaotic oscillators interconnected via a second order dynamic coupling. The design of the proposed coupling is inspired in the ancient synchronization experiment of synchronized pendulum clocks, as described by the Dutch scientist Christiaan Huygens more than three centuries ago. It is demonstrated that the coupled chaotic systems may exhibit not only complete synchronization, but also mixed synchronization—some states synchronize in anti-phase whereas other states synchronize in-phase. In fact, a transition from complete synchronization to mixed synchronization or viceversa can be induced by just changing a single parameter in the coupling. Additionally, the stability of the synchronous solution is investigated by using the Master Stability Function approach and the largest transverse Lyapunov exponent. The Lorenz system is considered as particular application example. Finally, the performance of the proposed synchronization scheme is illustrated with computer simulations and validated by means of experiments using electronic circuits.