网络的平均度对复杂网络上动力学行为的影响

Effects of Average Degree on Network Dynamics

本文考察了网络的平均度对网络上的同步、博弈和传播动力学行为的影响。结果发现,随着平均度的增大,复杂网络会表现出更优的同步能力,在博弈中合作率会显著提升,在传播动力学中传播范围会明显扩大。但平均度对这几种动力学行为的影响强度却是不同的:对于同步来说,平均度比较小时效果更明显;对于博弈来说,合作概率随着平均度的增加线性增加;而对于传播来说,平均度较大时效果较显著。另外,本文还发现一个有趣的现象:度分布异质性很强的无标度网络表现出比预想中强得多的同步能力,尤其是对于耦合矩阵是归一化的拉普拉斯矩阵的情况。本文定量地分析了平均度对网络上的几个重要动力学行为的影响,进一步深化了人们对平均度的影响的认识。

The effects of average degree on synchronization,games and information spreading are studied.The results show that increasing the average degree will enhance the synchronizability of networks,increase the cooperation rate in network,games and enlarge the spreading scale of information.Besides,it＇s found that the scale-free networks whose degree distribution is heterogeneous,show the synchronizability is strong when the coupling matrix is Laplacian and it is even stronger when the coupling matrix is normalized Laplacian.This study sheds light on the effects of average degree on the dynamical behavior of complex networks,which may be useful for the regulation of the corresponding dynamical behavior.