Synchronizability of time-varying structured duplex dynamical networks with different intra-layer rewiring mechanisms

Global synchronizability of duplex networks induced by three different intra-layer rewiring mechanisms is explored in this paper. The rewiring mechanisms are named as model-preserving rewiring (MPR), simply direct rewiring (SDR), and degree-preserving rewiring (DPR), respectively. It is found that high switching frequencies will certainly enhance global synchronizability for WS-WS duplex networks (i.e., each layer is independently formed by the algorithm proposed by Watts and Strogatz for generating small-world networks), ER-ER duplex networks (i.e., each layer is independently generated by the algorithm proposed by Erdos and Renyi) and BA-BA duplex networks (i.e., each layer is independently formed by the classical BA algorithm). Namely, the faster the intra-layer couplings are reconnected, the faster the duplex networks reach global synchronization. Furthermore, we find that by increasing the intra- or inter-coupling strengths, the WS-WS time-varying network's global synchronizability is enhanced. Take the WS-WS time-varying network as an example, we find that SDR mechanism has greater impact on global synchronizability than MPR mechanism and DPR mechanism. The related dynamical networks can arrive at synchronization faster by SDR than by MPR or DPR. Thus, we only study the effects of SDR on ER-ER duplex networks and BA-BA duplex networks. In addition, we obtain the fact via numerical simulations that, switching intra-layer coupling topologies under SDR mechanism has the greatest impact on the BA-BA duplex network, followed by the ER-ER network, and has the weakest influence on the WS-WS duplex network in terms of improving the global synchronizability when all the intra-layer networks are sparse and have the same average degree. Finally, the global synchronizability of WS-WS and BA-BA time-varying networks is improved compared with static duplex networks, the reason being that the networks tend to be randomized under SDR according to analysis of the networks' average clustering coefficients and degree distributions.