Eigenvalue Spectrum and Synchronizability of Double-Layer Directed Ring Networks
Ping Wu, Zhen Jia, Feimei Yang, Jiaquan Huang · Journal of Applied Mathematics and Physics · 2021
The synchronizability of multiplex undirected regular networks has been intensively studied based on the study of the synchronizability of single-layer networks. However, most real networks are characterized by some degree of directionality. So multiplex directed networks can better explain the synchronizability phenomenon. Here, based on the theory of master stability function (MSF), we study the eigenvalue spectrum and synchronizability of double-layer inter-layer directed ring networks (Networks-A) and double-layer intra-layer directed ring networks (Networks-B). The eigenvalue spectrum of the supra-Laplacian matrix of the networks is rigorously derived, and the influence of the networks structure parameters on the network’s synchronizability is analyzed. The correctness of the theory is further verified by numerical simulation analysis. Finally, the synchronizability of four kinds of double-layer ring networks with different coupling modes, namely, Networks-A, Networks-B, Networks-C (double-layer undirected ring networks), and Networks-D (double-layer undirected inter-layer random-added-edge ring networks), is compared and the results can provide guidance for constructing the optimal synchronization network.