Chaos 16, 015104 (2006) Changsong Zhou and Jurgen Kurths 这是一篇我看到的极出色的文章,所研究的复杂网络上的分层同步(我就直译了)问题对识别网络的拓扑结构具有启发性。PRE80,016116(2009)也正是基于此,明确提出了用来网络探测。在没有看到更早的文献之前,我先当它是利用动力学来探测网络度分布的第一文了。如此说,EPL82,68001(2008)可能要觉得有点冤,因为那里宣称是首次。但在仔细阅读这三文章之后,我还是认为这里闪烁的“原创性”更明亮!
文章的摘要:We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function.
3.“Interestingly, the stability analysis of the CS state can be adopted to provide an understanding of the hierarchical synchronization.”这是在简介结尾时说的一句话,可能是对应II(E)部分的,平均场分析。因为这一部分的分析方法与MSF相似。不同的是normalized耦合强度是结点度的显函数,且由之可知度大的结点耦合强度也大。所以可想而知的是有权连接对所讨论的对象也有很大的影响。
4.文章最后一句“Our present interest is on self-organization of structures and dynamics due to the interplay between them”令人浮想连翩。