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By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes, so this kind of networks is named as the weight-degree correlated (WDC) network. In scheme-II, the link weights are randomly assigned to each link regardless of the node degrees, so this kind of networks is named as the weight-degree uncorrelated (WDU) network. Interestingly, it is found that by increasing a parameter that governs the weight distribution, the onset of synchronization in WDC network is monotonically enhanced, while in WDU network there is a reverse in the synchronization performance. We investigate this phenomenon from the viewpoint of gradient network, and explain the contrary roles of coupling gradient on network synchronization: gradient promotes synchronization in WDC network, while deteriorates synchronization in WDU network. The findings highlight the fact that, besides the link weight, the correlation between the weight and node degree is also important to the network dynamics.
Network topology plays an important role in governing the collective dynamics. Partial synchronization (PaS) on regular networks with a few non-local links is explored. Different PaS patterns out of the symmetry breaking are observed for different wa
The behavior of two unidirectionally coupled chaotic oscillators near the generalized synchronization onset has been considered. The character of the boundaries of the generalized synchronization regime has been explained by means of the modified system
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or asymmetries in s
Previous work shows that the mean first-passage time (MFPT) for random walks to a given hub node (node with maximum degree) in uncorrelated random scale-free networks is closely related to the exponent $gamma$ of power-law degree distribution $P(k)si
The recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account. Here we focus on various generalizations of the clustering coeffici