A forward step for adaptive synchronization in directed complex networks

Synchronization in complex networks has been widely investigated recently. Almost all the existing conditions for reaching certain dynamics in complex networks require the global spectrum information of the network. A challenging problem for how the network structure affects the network dynamics in a distributed way especially with directed topologies is still unreleased in the recent decade. In particular, what kind of network structure or coupling weights in the general directed complex networks are very critical and how to change these weights in a local setting to achieve the desired behavior? This paper aims to solve this challenging problem.