Synchronizability of Generalized Two-layer Networks with Different Layer Topologies

This paper focuses on a generalized two-layer network and its synchronizability, which randomly generate different topologies at each layer. This kind of network can better describe some irregular networks in reality. From the master stability function method of network synchronization analysis, we estimate the largest eigenvalue and the lowest nonzero eigenvalue of the supra-Laplacian matrix. Then, the influence of node coupling strength on the synchronizability of generalized two-layer networks is analyzed. We obtain that the enhancement of node coupling strength can promote network synchronization in bounded and unbounded synchronization regions. In the end, we perform numerical simulations based on theoretical analysis. The numerical results also show that the more nodes, the stronger the synchronizability under the unbounded synchronization region, and the opposite is true for the bounded synchronization region. The results have a certain guiding significance for the synchronous application of general network in reality.