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 Pinning Two Nonlinearly Coupled Complex Networks with an Asymmetrical Coupling Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
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.

scholarly journals Impulsive Pinning Markovian Switching Stochastic Complex Networks with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Chen Xu ◽  
Jingyi Wang ◽  
Jianwen Feng ◽  
Yi Zhao
Keyword(s):  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Functional Method ◽  
Markovian Switching ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Stochastic Complex Networks

The synchronization problem of stochastic complex networks with Markovian switching and time-varying delays is investigated by using impulsive pinning control scheme. The complex network possesses noise perturbations, Markovian switching, and internal and outer time-varying delays. Sufficient conditions for synchronization are obtained by employing the Lyapunov-Krasovskii functional method, Itö's formula, and the linear matrix inequality (LMI). Numerical examples are also given to demonstrate the validity of the theoretical results.

scholarly journals Exponential Synchronization of Inertial Cohen–Grossberg Neural Networks with Time-Varying Delays via Periodically Intermittent Control

2020 ◽  
Vol 15 (2) ◽  
pp. 15
Author(s):  
Qing Ding ◽  
Yinfang Song
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Exponential Synchronization ◽  
Intermittent Control ◽  
Time Varying ◽  
Periodically Intermittent Control ◽  
Synchronization Problem ◽  
Control Schemes ◽  
Inequality Techniques

This paper deals with the exponential synchronization problem of inertial Cohen–Grossberg neural networks with time-varying delays under periodically intermittent control. In light of Lyapunov–Krasovskii functional method and inequality techniques, some sufficient conditions are attained to ensure the exponential synchronization of the master-slave system on the basis of p-norm. Meanwhile, the periodically intermittent control schemes are designed. Finally, in order to verify the effectiveness of theoretical results, some numerical simulations are provided.

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 Outer Synchronization between Complex Networks with Nonlinear Time-Delay Characteristics and Time-Varying Topological Structures

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xinli Fang ◽  
Qiang Yang ◽  
Wenjun Yan
Keyword(s):  
Time Delay ◽  
Complex Networks ◽  
Lyapunov Stability Theory ◽  
Time Varying ◽  
Outer Synchronization ◽  
Topological Structures ◽  
Synchronization Problem ◽  
Adaptive Control Strategy ◽  
And Control ◽  
Time Invariant

This paper exploits the network outer synchronization problem in a generic context for complex networks with nonlinear time-delay characteristics and nonidentical time-varying topological structures. Based on the classic Lyapunov stability theory, the synchronization criteria and adaptive control strategy are presented, respectively, by adopting an appropriate Lyapunov-Krasovskii energy function and the convergence of the system error can also be well proved. The existing results of network outer synchronization can be obtained by giving certain conditions, for example, treating the coupling matrices as time-invariant, and by applying the suggested generic synchronization criteria and control scheme. The numerical simulation experiments for networks scenarios with dynamic chaotic characteristics and time-varying topologies are carried out and the result verifies the correctness and effectiveness of the proposed control solution.

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 Mean-Square Exponential Synchronization of Markovian Switching Stochastic Complex Networks with Time-Varying Delays by Pinning Control

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Jingyi Wang ◽  
Chen Xu ◽  
Jianwen Feng ◽  
Man Kam Kwong ◽  
Francis Austin
Keyword(s):  
Complex Networks ◽  
Control Method ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Exponential Synchronization ◽  
Markovian Switching ◽  
Linear Matrix ◽  
Time Varying ◽  
Mean Square ◽  
Stochastic Complex Networks

This paper investigates the mean-square exponential synchronization of stochastic complex networks with Markovian switching and time-varying delays by using the pinning control method. The switching parameters are modeled by a continuous-time, finite-state Markov chain, and the complex network is subject to noise perturbations, Markovian switching, and internal and outer time-varying delays. Sufficient conditions for mean-square exponential synchronization are obtained by using the Lyapunov-Krasovskii functional, Itö’s formula, and the linear matrix inequality (LMI), and numerical examples are given to demonstrate the validity of the theoretical results.

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.

scholarly journals Outer Synchronization of Drive-Response Complex-Valued Complex Networks via Intermittent Pinning Control

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xuefei Wu ◽  
Jianwen Feng ◽  
Zhe Nie
Keyword(s):  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Functional Method ◽  
Exponential Synchronization ◽  
Time Varying ◽  
Response System ◽  
Lyapunov Functional Method ◽  
Complex Valued ◽  
Response Complex

This paper is concerned with the outer exponential synchronization of the drive-response complex dynamical networks subject to time-varying delays. The dynamics of nodes is complex valued, the interactions among of the nodes are directed, and the two coupling matrices in the drive system and the response system are also different. The intermittent pinning control is proposed to achieve outer exponential synchronization in the aperiodical way. Some novel sufficient conditions are derived to guarantee outer exponential synchronization of the considered complex-valued complex networks by using the Lyapunov functional method. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed control protocols.

scholarly journals Adaptive Synchronization of Complex Networks with Mixed Probabilistic Coupling Delays via Pinning Control

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jian-An Wang
Keyword(s):  
Complex Networks ◽  
Pinning Control ◽  
Adaptive Synchronization ◽  
Time Varying ◽  
Feedback Controllers ◽  
Adaptive Feedback ◽  
Network Nodes ◽  
Coupling Delay ◽  
Low Dimensional ◽  
Theoretical Results

The problem of synchronization for a class of complex networks with probabilistic time-varying coupling delay and distributed time-varying coupling delay (mixed probabilistic time-varying coupling delays) using pinning control is investigated in this paper. The coupling configuration matrices are not assumed to be symmetric or irreducible. By adding adaptive feedback controllers to a small fraction of network nodes, a low-dimensional pinning sufficient condition is obtained, which can guarantee that the network asymptotically synchronizes to a homogenous trajectory in mean square sense. Simultaneously, two simple pinning synchronization criteria are derived from the proposed condition. Numerical simulation is provided to verify the effectiveness of the theoretical results.

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