# Optimal Tree for Both Synchronizability and Converging Time - Nonlinear Sciences > Chaotic Dynamics

Abstract: It has been proved that the spanning tree from a given network has theoptimal synchronizability, which means the index $R=\lambda {N}-\lambda {2}$reaches the minimum 1. Although the optimal synchronizability is correspondingto the minimal critical overall coupling strength to reach synchronization, itdoes not guarantee a shorter converging time from disorder initialconfiguration to synchronized state. In this letter, we find that it is thedepth of the tree that affects the converging time. In addition, we present asimple and universal way to get such an effective oriented tree in a givennetwork to reduce the converging time significantly by minimizing the depth ofthe tree. The shortest spanning tree has both the maximal synchronizability andefficiency.

Author: An Zeng, Yanqing Hu, Zengru Di

Source: https://arxiv.org/