Synchronization in complex networks with blinking interactions

We propose a new model of small-world networks of cells with a time-varying coupling and study its synchronization properties. In each time interval of length τ such a coupling is switched on with probability p and the corresponding switching random variables are independent for different links and for different times. At each moment the coupling corresponds to a small-world graph, but the shortcuts change from time interval to time interval, which is a good model for many real-world dynamical networks. We prove that for the blinking model, a few random shortcut additions significantly lower the synchronization threshold together with the effective characteristic path length. Short interactions between cells, as in the blinking model, are important in practice. To cite prominent examples, computers networked over the Internet interact by sending packets of information, and neurons in our brain interact by sending short pulses, called spikes. The rare interaction between arbitrary nodes in the network greatly facilitates synchronization without loading the network much. In this respect, we believe that it is more efficient than a structure of fixed random connections.