Synchronizability of Duplex Networks

This brief presents some rules and properties about synchronizability of duplex networks composed of two networks interconnected by two links. For a specific duplex network composed of two star networks, analytical expressions containing the largest and smallest nonzero eigenvalues of the (weighted) Laplacian matrix, the interlink weight, and the network size are given for three different interlayer connection patterns. It is shown that connection patterns have great influence on the ability of the duplex system to synchronize, and connecting high-degree nodes is the most effective way to achieve synchronization, while connecting low-degree nodes is the least. Numerical examples are also provided to verify the effectiveness of theoretical analysis. This work sheds new light on understanding synchronizability of groups of interconnected networks or networks of networks (NONs). Particularly, in the design of circuit networks such as power grids, the findings can facilitate engineers with optimal selections of interconnection patterns and parameter assignments, in terms of optimizing the stability of desired synchronous states and minimizing control cost.