Synchronization of two Rössler Systems with Switching Coupling

In this paper, we study a system of two Rössler oscillators coupled through a time-varying link, periodically switching between two values. We analyze the system behavior with respect to the switching frequency. By applying an averaging technique under the hypothesis of high switching frequency, we find that, although each value of the coupling is not suitable for synchronization, switching between the two at a high frequency makes synchronization possible. However, we also find windows of synchronization below the value predicted by this technique, and we develop a master stability function to explain the appearance of these windows. The spectral properties of the system provide a useful tool for understanding the dynamics and synchronization failure in some intervals of the switching frequency. An experimental setup based on a digital/analog circuit is also presented showing experimental results which are in good agreement with the numerical analysis presented.