Cluster synchronization of community network with distributed time delays via impulsive control

doi:10.1088/1674-1056/25/11/110501

中国物理B ›› 2016, Vol. 25 ›› Issue (11): 110501-110501.doi: 10.1088/1674-1056/25/11/110501

Cluster synchronization of community network with distributed time delays via impulsive control

Hui Leng(冷卉), Zhao-Yan Wu(吴召艳)

College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China

收稿日期:2016-05-06 修回日期:2016-08-18 出版日期:2016-11-05 发布日期:2016-11-05
通讯作者: Zhao-Yan Wu E-mail:zhywu@jxnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61463022), the Natural Science Foundation of Jiangxi Province, China (Grant No. 20161BAB201021), and the Natural Science Foundation of Jiangxi Educational Committee, China (Grant No. GJJ14273).

Cluster synchronization of community network with distributed time delays via impulsive control

Hui Leng(冷卉), Zhao-Yan Wu(吴召艳)

College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China

Received:2016-05-06 Revised:2016-08-18 Online:2016-11-05 Published:2016-11-05
Contact: Zhao-Yan Wu E-mail:zhywu@jxnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61463022), the Natural Science Foundation of Jiangxi Province, China (Grant No. 20161BAB201021), and the Natural Science Foundation of Jiangxi Educational Committee, China (Grant No. GJJ14273).

摘要/Abstract

摘要： Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations. A community network with distributed time delays is investigated in this paper. For achieving cluster synchronization, an impulsive control scheme is introduced to design proper controllers and an adaptive strategy is adopted to make the impulsive controllers unified for different networks. Through taking advantage of the linear matrix inequality technique and constructing Lyapunov functions, some synchronization criteria with respect to the impulsive gains, instants, and system parameters without adaptive strategy are obtained and generalized to the adaptive case. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

关键词: cluster synchronization, community network, distributed time delay, impulsive control

Abstract: Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations. A community network with distributed time delays is investigated in this paper. For achieving cluster synchronization, an impulsive control scheme is introduced to design proper controllers and an adaptive strategy is adopted to make the impulsive controllers unified for different networks. Through taking advantage of the linear matrix inequality technique and constructing Lyapunov functions, some synchronization criteria with respect to the impulsive gains, instants, and system parameters without adaptive strategy are obtained and generalized to the adaptive case. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Key words: cluster synchronization, community network, distributed time delay, impulsive control

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

05.45.-a (Nonlinear dynamics and chaos)

冷卉, 吴召艳. Cluster synchronization of community network with distributed time delays via impulsive control[J]. 中国物理B, 2016, 25(11): 110501-110501.

Hui Leng(冷卉), Zhao-Yan Wu(吴召艳). Cluster synchronization of community network with distributed time delays via impulsive control[J]. Chin. Phys. B, 2016, 25(11): 110501-110501.

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Cluster synchronization of community network with distributed time delays via impulsive control

Cluster synchronization of community network with distributed time delays via impulsive control

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