On Synchronization of Pinning-Controlled Networks with Reducible and Asymmetric Coupling Matrix

• 作者: Hui Feng Jianwen Feng Xuan Zhou Yi Zhao
• 来源期刊: 通讯与网络(英文)
• 学科: 数学
• 关键词: Globally SYNCHRONIZATION Complex NETWORKS PINNING Control REDUCIBLE and ASYMMETRIC Matrix
• 年，卷（期）: 2011,（2）
• 页码范围: 118-126
• 页数: 9页
• 分类号: O1

摘要

This paper investigates the synchronization of directed networks whose coupling matrices are reducible and asymmetrical by pinning-controlled schemes. A strong sufficient condition is obtained to guarantee that the synchronization of the kind of networks can be achieved. For the weakly connected network, a method is presented in detail to solve two challenging fundamental problems arising in pinning control of complex networks: (1) How many nodes should be pinned? (2) How large should the coupling strength be used in a fixed complex network to realize synchronization? Then, we show the answer to the question that why all the diagonal block matrices of Perron-Frobenius normal matrices should be pinned? Besides, we find out the relation between the Perron-Frobenius normal form of coupling matrix and the differences of two synchronization conditions for strongly connected networks and weakly connected ones with linear coupling configuration. Moreover, we propose adaptive feedback algorithms to make the coupling strength as small as possible. Finally, numerical simulations are given to verify our theoretical analysis.