Hybrid synchronization of the general delayed and non-delayed complex dynamical networks via pinning control

In this paper, we study the synchronization problem for nonlinearly coupled complex dynamical networks on time scales. To achieve synchronization for nonlinearly coupled complex dynamical networks on time scales, a pinning control strategy is designed. Some pinning synchronization criteria are established for nonlinearly coupled complex dynamical networks on time scales, which guarantee the whole network can be pinned to some desired state. The model investigated in this paper generalizes the continuous-time and discrete-time nonlinearly coupled complex dynamical networks to a unique and general framework. Moreover, two numerical examples are given for illustration and verification of the obtained results.

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Generation of clusters in complex dynamical networks via pinning control

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8113/41/50/505101 ◽

2008 ◽

Vol 41 (50) ◽

pp. 505101 ◽

Cited By ~ 22

Author(s):

Kezan Li ◽

Michael Small ◽

Xinchu Fu

Keyword(s):

Pinning Control ◽

Complex Dynamical Networks ◽

Dynamical Networks

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Synchronization of fractional-order complex dynamical networks via periodically intermittent pinning control

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2017.06.025 ◽

2017 ◽

Vol 103 ◽

pp. 357-363 ◽

Cited By ~ 27

Author(s):

Hong-Li Li ◽

Cheng Hu ◽

Haijun Jiang ◽

Zhidong Teng ◽

Yao-Lin Jiang

Keyword(s):

Fractional Order ◽

Pinning Control ◽

Complex Dynamical Networks ◽

Order Complex ◽

Dynamical Networks

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Pinning Two Nonlinearly Coupled Complex Networks with an Asymmetrical Coupling Matrix

Discrete Dynamics in Nature and Society ◽

10.1155/2013/959368 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Jianwen Feng ◽

Ze Tang ◽

Jingyi Wang ◽

Yi Zhao

Keyword(s):

Complex Networks ◽

Lyapunov Stability Theory ◽

Pinning Control ◽

Feedback Controllers ◽

Dynamical Networks ◽

Synchronization Problem ◽

Response Network ◽

Control Schemes ◽

Hybrid Synchronization ◽

Theoretical Results

This paper addresses the hybrid synchronization problem in two nonlinearly coupled complex networks with asymmetrical coupling matrices under pinning control schemes. The hybrid synchronization of two complex networks is the outer antisynchronization between the driving network and the response network while the inner complete synchronization in the driving network and the response network. We will show that only a small number of pinning feedback controllers acting on some nodes are effective for synchronization control of the mentioned dynamical networks. Based on Lyapunov Stability Theory, some simple criteria for hybrid synchronization are derived for such dynamical networks by pinning control strategy. Numerical examples are provided to illustrate the effectiveness of our theoretical results.

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Synchronization control of complex dynamical networks with piecewise constant arguments

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331218759494 ◽

2018 ◽

Vol 41 (2) ◽

pp. 540-551 ◽

Cited By ~ 1

Author(s):

Tianhu Yu ◽

Menglong Su

Keyword(s):

Impulsive Control ◽

Lyapunov Stability Theory ◽

Pinning Control ◽

Complex Dynamical Networks ◽

Control Law ◽

Dynamical Networks ◽

Piecewise Constant Arguments ◽

Piecewise Constant ◽

Synchronization Problem ◽

Theoretical Results

The pinning synchronization problem is investigated for complex dynamical networks with hybrid coupling via impulsive control. Based on the Lyapunov stability theory, some novel synchronization criteria are derived and an impulsive pinning control law is proposed. By introducing a differential inequality for systems with piecewise constant arguments, it is not necessary to establish any relationship between the norms of the error states with or without piecewise constant arguments. Typical numerical examples are utilized to illustrate the validity and improvements as regards conservativeness of the theoretical results.

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