scholarly journals New Pinning Synchronization of Complex Networks with Time-Varying Coupling Strength and Nondelayed and Delayed Coupling

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Guoliang Wang ◽  
Zhongbao Yue ◽  
Feng Wang
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Coupling Strength ◽  
Time Varying ◽  
Numerical Example ◽  
Synchronization Problem ◽  
Delayed Coupling

The pinning synchronization problem for a class of complex networks is studied by a stochastic viewpoint, in which both time-varying coupling strength and nondelayed and delayed coupling are included. Different from the traditionally similar methods, its interval is separated into two subintervals and described by a Bernoulli variable. Both bounds and switching probability of such subintervals are contained. Particularly, the nondelayed and delayed couplings occur alternately in which another independent Bernoulli variable is introduced. Then, a new kind of pinning controller without time-varying coupling strength signal is developed, in which only its bounds and probabilities are contained. When such probabilities are unavailable, two different kinds of adaption laws are established to make the complex network globally synchronous. Finally, the validity of the presented methods is proved through a numerical example.

Complex projection synchronization of fractional order uncertain complex-valued networks with time-varying coupling

2019 ◽  
Vol 33 (29) ◽  
pp. 1950351 ◽  
Author(s):  
Dawei Ding ◽  
Xiaolei Yao ◽  
Hongwei Zhang
Keyword(s):  
Fractional Order ◽  
Coupling Strength ◽  
Dynamic Networks ◽  
Sufficient Conditions ◽  
Feedback Gain ◽  
Time Varying ◽  
Order Complex ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Complex Valued

In this paper, the complex projection synchronization problem of fractional complex-valued dynamic networks is investigated. Considering the time-varying coupling and unknown parameters of the fractional order complex network, several decentralized adaptive strategies are designed to adjust the coupling strength and controller feedback gain in order to investigate the complex projection synchronization problem of the system. Moreover, based on the designed identification law, the uncertain parameters in the network can be estimated. Using adaptive law which balances the time-varying coupling strength and the feedback gain of the controller, some sufficient conditions are obtained for the complex projection synchronization of complex networks. Finally, numerical simulation examples are provided to illustrate the efficiency of the complex projection synchronization strategies of the fractional order complex dynamic networks.

scholarly journals Finite-Time Bounded Synchronization of the Growing Complex Network with Nondelayed and Delayed Coupling

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Yuhua Xu ◽  
Jincheng Zhang ◽  
Wuneng Zhou ◽  
Dongbing Tong
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Finite Time ◽  
Time Synchronization ◽  
Stable Theory ◽  
Complex Dynamical Network ◽  
Numerical Examples ◽  
Delayed Coupling ◽  
Growing Networks ◽  
Theoretical Results

The objective of this paper is to discuss finite-time bounded synchronization for a class of the growing complex network with nondelayed and delayed coupling. In order to realize finite-time synchronization of complex networks, a new finite-time stable theory is proposed; effective criteria are developed to realize synchronization of the growing complex dynamical network in finite time. Moreover, the error of two growing networks is bounded simultaneously in the process of finite-time synchronization. Finally, some numerical examples are provided to verify the theoretical results established in this paper.

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.

THE OPTIMUM OF SYNCHRONIZABILITY IN COMPLEX NETWORKS

2010 ◽  
Vol 21 (10) ◽  
pp. 1255-1261 ◽  
Author(s):  
PEI-JIE MA ◽  
BING-HONG WANG
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Coupling Strength ◽  
Laplacian Matrix ◽  
Weight Matrix ◽  
Exact Form ◽  
Eigenvalues And Eigenvectors ◽  
Optimal Network ◽  
The One ◽  
Insight Into

In this brief report, we investigate the synchronizability of the complex network. In order to optimize the synchronizability, we propose a method by introducing a weight matrix, which makes the synchronized states stable for the widest range of the overall coupling strength. We give a proof in mathematics and gain the exact form of the weight matrix, which is equal to Lβ. Matrix L is the one that describes the optimal network and matrix β is constructed by the eigenvalues and eigenvectors of the usual Laplacian matrix. This result may provide us insight into the synchronization of complex network more deeply.

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.

scholarly journals Synchronization in Time-Varying and Evolving Complex Networks

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1939
Author(s):  
Gualberto Solís-Perales ◽  
José Luis Zapata ◽  
Guillermo Obregón-Pulido
Keyword(s):  
Complex Networks ◽  
Exponential Stability ◽  
Coupling Strength ◽  
Interconnected Systems ◽  
Time Varying ◽  
Numerical Examples ◽  
Dynamical Complex Networks

In this contribution, we present the synchronization in dynamical complex networks with varying couplings. We identify two kinds of variations—(i) Non autonomous (Time-varying) couplings: where the coupling strength depends exclusively on time, (ii) Autonomous or Varying couplings (evolution) where the coupling strength depends on the behavior of the interconnected systems. The coupling strength in (i) is exogenous whereas in (ii) the coupling strength is endogenous and is defined by the states of the systems in the nodes. The exponential stability of the synchronization is ensured for the non autonomous couplings, due to the imposition of the coupling strength. Whereas, in the case of evolutionary couplings the exponential stability of the synchronization is not guaranteed for all time, due to the couplings are not controlled or imposed. We present an overview of these features in complex networks and illustrated by means of numerical examples.

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