scholarly journals Complex Projective Synchronization in Drive-Response Stochastic Complex Networks by Impulsive Pinning Control

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xuefei Wu ◽  
Zhe Nie
Keyword(s):  
Sufficient Conditions ◽  
Pinning Control ◽  
Projective Synchronization ◽  
Adaptive Feedback ◽  
Response Network ◽  
Control Scheme ◽  
Coupled Networks ◽  
General Drive ◽  
Stochastic Complex Networks ◽  
Complex Projective

The complex projective synchronization in drive-response stochastic coupled networks with complex-variable systems is considered. The impulsive pinning control scheme is adopted to achieve complex projective synchronization and several simple and practical sufficient conditions are obtained in a general drive-response network. In addition, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical simulations are provided to show the effectiveness and feasibility of the proposed methods.

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 Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ze Tang ◽  
Jianwen Feng
Keyword(s):  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Control Cost ◽  
Synchronization Problem ◽  
Delayed Coupling ◽  
Control Scheme ◽  
Successful Control ◽  
Synchronization Pattern

We focus on the cluster synchronization problem for a kind of general networks with nondelayed and delayed coupling. Based on the pinning control scheme, a small fraction of the nodes in each cluster are pinned for successful control, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the cluster synchronization pattern for all initial values by means of the Lyapunov stability theorem and linear matrix inequalities (LMIs). By using the adaptive update law, relative smaller control gains are obtained, and hence the control cost can be substantially lower. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.

The Control of a Neural Complex Network

2014 ◽  
Vol 687-691 ◽  
pp. 444-446
Author(s):  
Fan Di Zhang
Keyword(s):  
Neural Network ◽  
Community Structure ◽  
Lyapunov Stability ◽  
Control Strategy ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Projective Synchronization ◽  
Cluster Synchronization ◽  
Special Cases

In this paper, the synchronization of a neural network with community structure is investigated. Cluster projective generalizes previously existing synchronization schemes. The cluster projective synchronization is more general that includes projective synchronization and cluster synchronization, as its special cases. The cluster projective synchronization of these networks is discussed via some pinning control strategy. Several sufficient conditions for the network to achieve cluster projective synchronization are derived based on Lyapunov stability theory. Numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed scheme.

scholarly journals Adaptive-Impulsive Control of the Projective Synchronization in Drive-Response Complex Dynamical Networks with Time-Varying Coupling

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Song Zheng
Keyword(s):  
Impulsive Control ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Projective Synchronization ◽  
Time Varying ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Hybrid Controller ◽  
The Stability ◽  
Response Complex

This paper investigates the projective synchronization (PS) of drive-response time-varying coupling complex dynamical networks with time delay via an adaptive-impulsive controlling method, in which the weights of links are time varying. Based on the stability analysis of impulsive control system, sufficient conditions for the PS are derived, and a hybrid controller, that is, an adaptive feedback controller with impulsive control effects, is designed. Numerical simulations are performed to verify the correctness and effectiveness of theoretical result.

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 Asymptotical Synchronization for Stochastic Complex Networks with Time-Delay and Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xueling Jiang ◽  
Shuijie Qin ◽  
Dongbing Tong ◽  
Liping Wang
Keyword(s):  
Time Delay ◽  
Complex Networks ◽  
Matrix Method ◽  
Stochastic Analysis ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Control Techniques ◽  
Stochastic Complex Networks

The problem of adaptive asymptotical synchronization is discussed for the stochastic complex dynamical networks with time-delay and Markovian switching. By applying the stochastic analysis approach and theM-matrix method for stochastic complex networks, several sufficient conditions to ensure adaptive asymptotical synchronization for stochastic complex networks are derived. Through the adaptive feedback control techniques, some suitable parameters update laws are obtained. Simulation result is provided to substantiate the effectiveness and characteristics of the proposed approach.

SYNCHRONIZATION OF COMPLEX-VARIABLE DYNAMICAL NETWORKS WITH COMPLEX COUPLING

2013 ◽  
Vol 24 (02) ◽  
pp. 1350007 ◽  
Author(s):  
ZHAOYAN WU ◽  
XINCHU FU
Keyword(s):  
Complex Variable ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Control Scheme ◽  
General Network ◽  
Adaptive Coupling ◽  
Theoretical Results

In this paper, synchronization of complex-variable dynamical networks with complex coupling is investigated. An adaptive feedback control scheme is adopted to design controllers for achieving synchronization of a general network with both complex inner and outer couplings. For a network with only complex inner or outer coupling, pinning control and adaptive coupling strength methods are adopted to achieve synchronization under some assumptions. Several synchronization criteria are derived based on Lyapunov stability theory. Numerical simulations are provided to verify the effectiveness of the theoretical results.

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 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.

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