Randomly Occurring Cluster Synchronization of Complex Networks via Adaptive Pinning Control

2021 ◽  
Author(s):  
Chenhui Jiang ◽  
Dong Ding ◽  
Jiancheng Zhang ◽  
Ze Tang
Keyword(s):  
Complex Networks ◽  
Pinning Control ◽  
Cluster Synchronization

scholarly journals Cluster Synchronization for Linearly Coupled Complex Networks with Identical and Nonidentical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yi Zhao ◽  
Jianwen Feng ◽  
Jingyi Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Adaptive Feedback ◽  
Numerical Examples ◽  
Control Schemes ◽  
Nonidentical Nodes ◽  
Theoretical Results

The cluster synchronization of linearly coupled complex networks with identical and nonidentical nodes is studied. Without assuming symmetry, we proved that these linearly coupled complex networks could achieve cluster synchronization under certain pinning control schemes. Sufficient conditions guaranteeing cluster synchronization for any initial values are derived by using Lyapunov function methods. Moreover, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical examples are given to illustrate our theoretical results.

scholarly journals Adaptive Cluster Synchronization of Complex Networks with Identical and Nonidentical Lur’e Systems

Electronics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 706
Author(s):  
Yue Gao ◽  
Dong Ding ◽  
Ze Tang
Keyword(s):  
Numerical Simulation ◽  
Continuous Function ◽  
Complex Networks ◽  
Control Strategy ◽  
Sufficient Conditions ◽  
Function Class ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Lur’E Systems ◽  
Control Schemes

This paper is devoted to investigating the cluster synchronization of a class of nonlinearly coupled Lur’e networks. A novel adaptive pinning control strategy is introduced, which is beneficial to achieve cluster synchronization of the Lur’e systems in the same cluster and weaken the directed connections of the Lur’e systems in different clusters. The coupled complex networks consisting of not only identical Lur’e systems but also nonidentical Lur’e systems are discussed, respectively. Based on the S-procedure and the concept of acceptable nonlinear continuous function class, sufficient conditions are obtained which prove that the complex dynamical networks can be pinned to the heterogeneous solutions for any initial values. In addition, effective and comparatively small control strengths are acquired by the designing of the adaptive updating algorithm. Finally, a numerical simulation is presented to illustrate the proposed theorems and the control schemes.

scholarly journals Cluster Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control

2011 ◽  
Vol 2011 ◽  
pp. 1-23 ◽  
Author(s):  
Jianwen Feng ◽  
Jingyi Wang ◽  
Chen Xu ◽  
Francis Austin
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Topological Structure ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
General Complex ◽  
Coupling Strengths ◽  
Theoretical Results

We consider a method for driving general complex networks into prescribed cluster synchronization patterns by using pinning control. The coupling between the vertices of the network is nonlinear, and sufficient conditions are derived analytically for the attainment of cluster synchronization. We also propose an effective way of adapting the coupling strengths of complex networks. In addition, the critical combination of the control strength, the number of pinned nodes and coupling strength in each cluster are given by detailed analysis cluster synchronization of a special topological structure complex network. Our theoretical results are illustrated by numerical simulations.

scholarly journals Cluster Synchronization of Stochastic Complex Networks with Markovian Switching and Time-Varying Delay via Impulsive Pinning Control

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xuan Zhou ◽  
Kui Luo
Keyword(s):  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Markovian Switching ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Control Scheme ◽  
Stochastic Complex Networks

This paper studies the cluster synchronization of a kind of complex networks by means of impulsive pinning control scheme. These networks are subject to stochastic noise perturbations and Markovian switching, as well as internal and outer time-varying delays. Using the Lyapunov-Krasovskii functional, Itö’s formula, and some linear matrix inequalities (LMI), several novel sufficient conditions are obtained to guarantee the desired cluster synchronization. At the end of this writing, a numerical simulation is given to demonstrate the effectiveness of those theoretical results.

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