2009/06/02 by An Zeng, A. Zeng, Y. Hu +3
Computer Science · Physics and Astronomy · #Minimum spanning tree #Network topology #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Shortest-path tree #Spanning tree #Synchronization (alternating current) #Topology (electrical circuits) #Tree (set theory) #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1209/0295-5075/87/48002
4 pages, 4 figures
arxiv created 2009/06/02 · openalex publication_date 2009/08/01 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
It has been proved that the spanning tree from a given network has optimal synchronizability, which means the index R =λ N /λ 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.