Issue
EPL
Volume 87, Number 4, August 2009
Article Number 48002
Number of page(s) 5
Section Interdisciplinary Physics and Related Areas of Science and Technology
DOI http://dx.doi.org/10.1209/0295-5075/87/48002
Published online 02 September 2009
EPL, 87 (2009) 48002
DOI: 10.1209/0295-5075/87/48002

Optimal tree for both synchronizability and converging time

A. Zeng, Y. Hu and Z. Di

Department of Systems Science, School of Management, Beijing Normal University - Beijing 100875, PRC

zdi@bnu.edu.cn

received 24 June 2009; accepted in final form 28 July 2009; published August 2009
published online 2 September 2009

Abstract
It has been proved that the spanning tree from a given network has optimal synchronizability, which means the index R = $\lambda _{N}/\lambda _{2}$ 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.

PACS
89.75.Hc - Networks and genealogical trees.
05.45.Xt - Synchronization; coupled oscillators.
89.75.-k - Complex systems.

© EPLA 2009