Comparison of Synchronization Ability of Four Types of Regular Coupled Networks

We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.