scholarly journals Cluster linear generalized outer synchronization in community networks via pinning control with two different switch periods

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Yuhong Liu ◽  
Hui Li ◽  
Qishui Zhong ◽  
Shouming Zhong
Keyword(s):  
Pinning Control ◽  
Community Networks ◽  
Outer Synchronization

scholarly journals Outer Synchronization of Complex Networks with Nondelayed and Time-Varying Delayed Couplings via Pinning Control or Impulsive Control

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianwen Feng ◽  
Sa Sheng ◽  
Ze Tang ◽  
Yi Zhao
Keyword(s):  
Complex Networks ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Time Varying ◽  
Network Nodes ◽  
Outer Synchronization ◽  
Synchronization Problem ◽  
Response Network ◽  
Control Schemes

The outer synchronization problem between two complex networks with nondelayed and time-varying delayed couplings via two different control schemes, namely, pinning control and impulsive control, is considered. Firstly, by applying pinning control to a fraction of the network nodes and using a suitable Lyapunov function, we obtain some new and useful synchronization criteria, which guarantee the outer synchronization between two complex networks. Secondly, impulsive control is added to the nodes of corresponding response network. Based on the generalized inequality about time-varying delayed different equation, the sufficient conditions for outer synchronization are derived. Finally, some examples are presented to demonstrate the effectiveness and feasibility of the results obtained in this paper.

scholarly journals Outer Synchronization of Complex-Variable Networks with Complex Coupling via Impulsive Pinning Control

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2110
Author(s):  
Yanjie Ji ◽  
Zhaoyan Wu
Keyword(s):  
Complex Variable ◽  
Function Method ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Pinning Control ◽  
Adaptive Strategy ◽  
Numerical Examples ◽  
Outer Synchronization ◽  
Estimation Algorithms ◽  
Lyapunov Function Method

In this paper, outer synchronization of complex-variable networks with complex coupling is considered. Sufficient conditions for achieving outer synchronization using static impulsive pinning controllers are first derived according to the Lyapunov function method and stability theory of impulsive differential equations. From these conditions, the necessary impulsive gains and intervals for given networks can be easily calculated. Further, an adaptive strategy is introduced to design universal controllers and avoid repeated calculations for different networks. Notably, the estimation algorithms of the impulsive gains and intervals are provided. Finally, three numerical examples are performed to verify the effectiveness of the main results.

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