【作者】 曾安； 胡延庆； 狄增如；

【Author】 An Zeng,Yanqing Hu,Zengru Di Department of Systems Science,School of Management,Beijing Normal University,Beijing 100875,P.R.China

【机构】 北京师范大学管理学院系统科学系；

【摘要】 前人研究结果显示,从一个给定网络中得到其生成树,这个结构的同步能力将最强。也就是说,同步指标R=λN/λ2达到其最小值1。虽然最优同步能力对应着网络所需的临界耦合权重最小,但是,最优同步能力并不能保证网络有较短的同步收敛时间。在这篇文章中,我们发现,生成树的深度是影响网络生成树的因素,并且给出了深度和收敛时间的关系。另外,我们提出了一种简单且普适的方法来找到这样的最短生成树。这样的最短生成树拥有最少的层级结构,所有它将拥有最优的同步能力和最短的收敛时间。更多还原

【Abstract】 It has been proved that the spanning tree from a given network has the optimal synchronizability,which means the index R = λN/λ2 reaches the minimum 1.Although the optimal synchronizability is corresponding to the minimal critical overall coupling strength to reach synchronization,it does not guarantee a shorter converging time from disorder initial configuration to synchronized state.In this letter,we find that the depth of the tree is the only factor that affects the converging time.The relation between the depth and the converging time is given as well.In addition,we present a simple and universal way to get such an effective oriented tree from a given network to reduce the converging time significantly by minimizing the depth of the tree.The shortest spanning tree has both maximal synchronizability and minimal converging time.更多还原