Temasek Laboratories, National University of Singapore, Singapore 117508, Singapore.
Chaos. 2011 Jun;21(2):025108. doi: 10.1063/1.3597646.
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 the node degree is also important to the network dynamics.
通过数值模拟，我们研究了在两种不同加权方案下，网络相振荡器同步的起始情况。在方案 I 中，链路权重与连接节点的度数之积相关联，因此这种网络被命名为权重-度相关（WDC）网络。在方案 II 中，链路权重随机分配给每个链路，而不考虑节点度数，因此这种网络被命名为权重-度不相关（WDU）网络。有趣的是，我们发现通过增加一个控制权重分布的参数，可以单调地增强 WDC 网络中的同步起始，而在 WDU 网络中，同步性能则出现反转。我们从梯度网络的角度研究了这一现象，并解释了耦合梯度对网络同步的相反作用：在 WDC 网络中，梯度促进同步，而在 WDU 网络中则会恶化同步。这些发现突出了这样一个事实，即除了链路权重之外，权重与节点度数之间的相关性对于网络动态也很重要。
