Synchronization in multilayer networks through different coupling mechanisms

In recent years, most studies of complex networks have focused on a single network and ignored the interaction of multiple networks, much less the coupling mechanisms between multiplex networks. In this paper we investigate synchronization phenomena in multilayer networks with nonidentical topological structures based on three specific coupling mechanisms:assortative, disassortative, and anti-assortative couplings. We find rich and complex synchronous dynamic phenomena in coupled networks. We also study the behavior of effective frequencies for layers I and II to understand the underlying microscopic dynamics occurring under the three different coupling mechanisms. In particular, the coupling mechanisms proposed here have strong robustness and effectiveness and can produce abundant synchronization phenomena in coupled networks.