| 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 | https://doi.org/10.1209/0295-5075/87/48002 | |
| Published online | 02 September 2009 | |
Optimal tree for both synchronizability and converging time
Department of Systems Science, School of Management, Beijing Normal University - Beijing 100875, PRC
Corresponding author: zdi@bnu.edu.cn
Received:
24
June
2009
Accepted:
28
July
2009
It has been proved that the spanning tree from a given network has optimal synchronizability, which means the index R = 
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
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