Enhancing synchrony in asymmetrically weighted multiplex networks

We uncover the transition scenarios for two different kinds of synchronization appearing in a multiplex network, namely intralayer and interlayer synchronization, considering different weighting mechanisms among the coupled oscillators. Particularly, we choose an unweighted Erdos-Renyi interaction topology and then the weights are associated to the edges depending on the ratio of the adjacent nodal degrees. While considering intralayer connectivity, whether stronger nodal influences are received from a high degree node or a low degree node, the networks are classified accordingly as hubs-attracting or hubs-repelling, respectively. The obtained synchronization phenomena considering these two networks are compared with that of the unweighted network. Our explorations reveal that the intralayer synchronization is greatly enhanced in case of hubs-attracting network whereas it is de-enhanced for hubs-repelling network compared to the unweighted network. The obtained numerical results are also verified by analytically deriving necessary stability conditions using master stability function approach. We also explain the synchrony phenomena through spectral analysis of the corresponding Laplacian matrices and find that higher heterogeneity among the input intensities of the nodes gives lesser synchronizability and vice-versa. Moreover, the sustainability of interlayer synchronization is also scrutinized against progressive removal of interlayer links following either increasing or decreasing degree sequence of the nodes. (C) 2020 Elsevier Ltd. All rights reserved.