无标度网络同步过程研究

Synchronization Process in Scale-free Networks

在以对称耦合振子为节点的无标度网络中,度的不均匀分布性对网络的全局同步具有抑制作用,使得其同步过程研究比一般连续耦合网络完全同步研究方法更为复杂。论文将非线性系统理论以及稳定性理论等应用到无标度网络同步过程研究中,在每一个节点上引入非线性动态方程,对同步误差的变分进行稳定性分析,来判断节点是否能同步,并分析其研究方法与一般连续耦合网络完全同步研究方法的不同。以Rssler振子构成的无标度网络作为对象进行仿真,仿真结果表明,度的不均匀分布性不仅导致无标度网络的同步性能下降,而且使得它的同步过程具有分层过渡的特点。

In symmetric coupled scale-free networks, the research methods of synchronization are much more complicated than the tradi- tional ones which research the global synchronization in complex networks, because the heterogeneity in the degree distribution inhibits global synchronization. This paper applies the nonlinear system theory and the stability theory to study the synchronization process in scale-free net- works. The approach is to introduce nonlinear dynamics on each node and then perform stability analysis to determine when the nodes syn- chronize, and analysis the differences of the research methods used in scale-free networks and general complex networks. The conclusion is shown that heterogeneity not only inhibits the global synchronization, but also leads to a hierarchical transition toward further synchroniza- tion. Besides the feature that global synchronization is impossible in scale-free networks should be taken into full account, when studying the synchronization in scale-free networks.