Synchronization Of Complex Networks Research Articles

Preassigned-time bipartite synchronization of complex networks with quantized couplings and stochastic perturbations

By using the preassigned-time (PAT) control method, this paper considers bipartite synchronization of complex networks (CNs) with quantized couplings and stochastic perturbations. According to the characteristics of CNs and bipartite synchronization, a new controller is designed. In the controller, some control parameters are switched with the information of the error system, and the linear feedback term is not considered. Based on the properties of the Weiner process, a PAT criterion is given to guarantee the stochastic bipartite synchronization of CNs with a different Lyapunov function. In order to compare, a fixed-time control is designed and a synchronization criterion is also established. Moreover, experimental results effectively demonstrate the correctness of the theoretical analysis.

Disturbance rejections and synchronization of fractional-order fuzzy complex networks

This paper deals with the problem of disturbance rejection and synchronization of fractional-order complex dynamical networks subject to nonlinear coupling strength and discontinuous nonlinear functions. Notably, the nonlinear coupling strength is linearised by using a well-known Takagi-Sugeno fuzzy approach. The considered system is transformed into a nominal form by employing the uncertainty and disturbance estimator-based control approach, which simplifies the control objective and improves the system performance. Second, the uncertainty and disturbance estimator is incorporated into the traditional feedback control scheme to reject the unknown disturbance and uncertainty. Then, the required synchronization conditions for both the discontinuous and continuous fractional-order systems are obtained by using Lyapunov stability and fractional calculus theories. Last, numerical examples are provided to illustrate the efficiency of the proposed control strategy, wherein it is shown that the system yields better satisfactory tracking performance and high robustness against possible disturbance and uncertainties and finite set of jump discontinuous nonlinear functions. Moreover, the selection of appropriate filter design is discussed for various kinds of disturbance signals.

Observer-based synchronisation control for discrete-time delayed switched complex networks with coding–decoding approach

ABSTRACT In this paper, we investigate the synchronisation control problem for a class of discrete-time switched complex networks with time-varying delays via a coding–decoding-based approach. An observer-based control scheme is proposed for each node by utilising the outputs of complex networks. The data are transmitted in a digital manner and only the sequence of finite coded signals is sent from the observer to the controller. We design a proper coding–decoding procedure for each node to ensure that the closed-loop networks achieve the expected synchronisation performance. By applying the average dwell-time switching strategy and a uniform quantisation approach, some criteria are firstly presented to ensure the detectability of the complex networks. Then sufficient conditions are provided for the existence of desired observer-based controller, guaranteeing the synchronisation of complex networks. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.

Novel Methods for the Global Synchronization of the Complex Dynamical Networks with Fractional-Order Chaotic Nodes

The global synchronization of complex networks with fractional-order chaotic nodes is investigated via a simple Lyapunov function and the feedback controller in this paper. Firstly, the GMMP method is proposed to obtain the numerical solution of the fractional-order nonlinear equation based on the relation of the fractional derivatives. Then, the new feedback controllers are proposed to achieve synchronization between the complex networks with the fractional-order chaotic nodes based on feedback control. We propose some new sufficient synchronous criteria based on the Lyapunov stability and a simple Lyapunov function. By the numerical simulations of the complex networks, we find that these synchronous criteria can apply to the arbitrary complex dynamical networks with arbitrary fractional-order chaotic nodes. Numerical simulations of synchronization between two complex dynamical networks with the fractional-order chaotic nodes are given by the GMMP method and the Newton method, and the results of numerical simulation demonstrate that the proposed method is universal and effective.

Finite-Time Projective Synchronization and Parameter Identification of Fractional-Order Complex Networks with Unknown External Disturbances

This paper is devoted to exploring the finite-time projective synchronization (FTPS) of fractional-order complex dynamical networks (FOCDNs) with unknown parameters and external disturbances. Based on the stability theory of fractional-order differential systems, synchronization criteria between drive-response networks were obtained and both the uncertain parameters and external disturbances were identified or conquered simultaneously. Moreover, the upper limit of the settling-time function was obtained. Finally, a numerical example was given to verify the effectiveness of the results.

Secure synchronization and identification for fractional complex networks with multiple weight couplings under DoS attacks

Secure synchronization and identification for fractional complex networks with multiple weight couplings under DoS attacks

Cluster synchronisation of nonlinear singular complex networks with multi-links and time delays

This paper investigates the cluster synchronisation problem of singular nonlinear networks with multi-links and time delays. A two-layer nonlinearly coupled multiplex model composed of many pairs of multi-link leader–follower subnets is introduced, which can more accurately reveal the structure between leader–follower layers. Based on Lyapunov stability theory, some stability criteria for cluster synchronisation are proposed by adaptive pinning control. Finally, numerical examples are employed to illustrate the effectiveness of the proposed methods.

Organization Synchronization in Response to Complex Project Delays: Network-Based Analysis

In response to frequent complex project delays, organization synchronization, a set of interactions, is a dynamic behavior that helps to restore the stability of complex projects after delays. However, few studies have figured out how organizations synchronize effectively in order to deal with delay issues. To solve this problem, this study first provides a preliminary list of CDFs and indices of organization interactions are also given. A total of 15 key CDFs and 10 interaction ways were refined according to a questionnaire survey. In addition, the complex network synchronization (CNS) theory was adopted to analyze the synchronizability and importance of nodes by comprehensively using multiple parameters. A complex metro project with 51 project organizations was used as a case study and we found that specific signal organizations synchronized through three effective interaction ways (meetings, discussion and study, and the Internet) to cope with six CDFs (safety accidents, prominent problems of land expropriation, unreasonable timelines by clients, improper construction designs, delayed payments, and high financial risks). This study contributes to defining organization synchronization, providing a feasible research framework for assessing network synchronizability and identifying signal organizations in complex projects, and guiding practitioners to effectively cope with delays by interactions between signal organizations.

Sampled-data synchronization of complex network based on periodic self-triggered intermittent control and its application to image encryption

The aim of this paper is to investigate exponential synchronization issue of time-varying multi-weights network with time delays (TMNTD) via periodic self-triggered intermittent sampled-data control. In particular, it is the first time to combine periodic self-triggered control and intermittent control with sampled-data, which has broader application prospects. Therein, self-triggered scheme is periodic judgment and aimed at intermittent control. And during control intervals in intermittent control, there is periodic sampled-data control. In addition, by applying tools of sampled-data control, intermittent control, event-driven control theory and stability analysis, some sufficient conditions are derived to guarantee exponential synchronization of TMNTD. After that, the theoretical results are utilized to research exponential synchronization issue of time-varying multi-weights Chua’s circuits with time delays. Meantime, numerical simulations are provided to demonstrate the validity of the theoretical results. Finally, an image encryption algorithm is designed as a practical application of the developed results.

Asymptotically local synchronization in interdependent networks with unidirectional interlinks.

Synchronization in complex networks has been investigated for decades. Due to the particularity of the interlinks between networks, the synchronization in interdependent networks has received increasing interest. Since the interlinks are not always symmetric in interdependent networks, we focus on the synchronization in unidirectional interdependent networks to study the control scheme. The mathematical model is put forward and some factors are taken into consideration, such as different coupling functions and strengths. Firstly, the feasibility of the control scheme is proved theoretically by using Lyapunov stability theory and verified by simulations. Then, we find that the synchronization could be maintained in one sub-network by utilizing our control scheme while the nodes in the other sub-network are in chaos. The result indicates that the influence of interlinks can be decreased and the proposed scheme can guarantee the synchronization in one sub-network at least. Moreover, we also discuss the robust of our control scheme against the cascading failure. The scheme is verified by simulations to be effective while the disturbances occur.

Fixed-Time Synchronization for Fuzzy-Based Impulsive Complex Networks

This paper mainly deals with the issue of fixed-time synchronization of fuzzy-based impulsive complex networks. By developing fixed-time stability of impulsive systems and proposing a T-S fuzzy control strategy with pure power-law form, some simple criteria are acquired to achieve fixed-time synchronization of fuzzy-based impulsive complex networks and the estimation of the synchronized time is given. Ultimately, the presented control scheme and synchronization criteria are verified by numerical simulation.

PID Control for Output Synchronization of Multiple Output Coupled Complex Networks

This article attempts to address output synchronization and <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> output synchronization problems for multiple output coupled complex networks (MOCCNs) under proportional-derivative (PD) and proportional-integral (PI) controllers. Firstly, two classes of MOCCNs without and with external disturbances are separately put forward. Secondly, based on the PD and PI control schemes, several output synchronization criteria for MOCCNs are formulated by using the Lyapunov functional method and inequality techniques. Thirdly, <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> output synchronization for MOCCNs is also studied with the help of the PD and PI controllers. Finally, two numerical examples are separately presented to demonstrate the validity of acquired theoretical results.

Global [formula omitted]-synchronization for nonlinear complex networks with unbounded multiple time delays and uncertainties via impulsive control

The global μ-synchronization problem of nonlinear drive–response complex networks with uncertainties is investigated in this paper. Unbounded multiple time delays, such as internal delays, coupling delays, and sampling delays in impulse instants are considered in our complex network model. The difficulties caused by these multiple time delays are overcome by introducing a generalized impulsive delayed comparison principle. A delayed impulsive controller is designed, and some novel synchronization criteria are derived in order to make drive–response complex networks achieve μ-synchronization. Compared with the existing related works, there is no restriction about impulse intervals and delays, as well as, the external coupling matrix is no longer needed to satisfy the dissipative coupling condition. Finally, two numerical simulations are shown to present the correctness of our theoretical results.

Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control

The finite-time synchronization of fractional-order multi-weighted complex networks (FMCNs) with uncertain parameters and external disturbances is studied. Firstly, based on fractional calculus characteristics and Lyapunov stability theory, quantized controllers are designed to guarantee that FMCNs can achieve synchronization in a limited time with and without coupling delay, respectively. Then, appropriate parameter update laws are obtained to identify the uncertain parameters in FMCNs. Finally, numerical simulation examples are given to validate the correctness of the theoretical results.

Synchronization of complex networks with hybrid delays based on event intermittent control

This paper studies the exponential synchronization problem for complex networks with hybrid delays via means of the event intermittent control (EIC) strategy. Compared with the traditional aperiodically intermittent control, the control instants and the rest instants are generated when the events occur, which is more in accordance with the actual situation. An modified lemma related to delays is derived without predesigning intermittent instants. Furthermore, some synchronization criteria with less conservatism are established in terms of linear matrix inequalities (LMIs). Meanwhile, it is also shown that Zeno behavior is excluded. Finally, simulations of a numerical example are given to verify the effectiveness of the proposed EIC strategy.

Finite-time passivity and synchronisation of complex networks with multiple output couplings

In this paper, we, respectively, discuss the finite-time passivity (FTP) and finite-time synchronisation (FTS) of multi-output coupled complex networks (MOCCNs) under directed topology and undirected topology. Firstly, through designing an appropriate state feedback controller and adaptive state feedback controller, using some inequality techniques, we investigate the FTP of MOCCNs. Furthermore, we study the relationship between the FTP and FTS of the MOCCNs, and establish the sufficient conditions to ensure that MOCCNs can realise FTS based on the result we get about FTP. Lastly, we verify the proposed FTP and FTS criteria using two numerical examples.

Identification and Synchronization of Switching Fractional-Order Complex Networks with Time-Varying Delays Based on a Fuzzy Method

Identification and Synchronization of Switching Fractional-Order Complex Networks with Time-Varying Delays Based on a Fuzzy Method

Exponential synchronization of complex networks via feedback control and periodically intermittent noise

In complex networks, asymptotic properties play an important role in modeling, analysis and design in both aspects of theory and practice. In this paper, our focus is on exponential synchronization for a class of complex networks. Under certain conditions, a feedback control and stochastic periodically intermittent noise are designed to synchronize the networks. Such synchronization scheme needs less control energy due to the usage of the intermittent noise. The threshold of intermittent rate for synchronization scheme is derived. Moreover, the noise states are observed in discrete-time mode, which reduces the complexity and the computation burden for continuous observations. The observation supremum is obtained by solving a transcendental equation. Finally, a simulation example is provided, and the comparison results with some existing methods illustrate the effectiveness and advantages of the proposed new design strategy.

Event-triggered delayed impulsive control for nonlinear systems with application to complex neural networks

This paper studies the Lyapunov stability of nonlinear systems and the synchronization of complex neural networks in the framework of event-triggered delayed impulsive control (ETDIC), where the effect of time delays in impulses is fully considered. Based on the Lyapunov-based event-triggered mechanism (ETM), some sufficient conditions are presented to avoid Zeno behavior and achieve globally asymptotical stability of the addressed system. In the framework of event-triggered impulse control (ETIC), control input is only generated at state-dependent triggered instants and there is no any control input during two consecutive triggered impulse instants, which can greatly reduce resource consumption and control waste. The contributions of this paper can be summarized as follows: Firstly, compared with the classical ETIC, our results not only provide the well-designed ETM to determine the impulse time sequence, but also fully extract the information of time delays in impulses and integrate it into the dynamic analysis of the system. Secondly, it is shown that the time delays in impulses in our results exhibit positive effects, that is, it may contribute to stabilizing a system and achieve better performance. Thirdly, as an application of ETDIC strategies, we apply the proposed theoretical results to synchronization problem of complex neural networks. Some sufficient conditions to ensure the synchronization of complex neural networks are presented, where the information of time delays in impulses is fully fetched in these conditions. Finally, two numerical examples are provided to show the effectiveness and validity of the theoretical results.

Cluster Synchronization for Multi-Weighted and Directed Complex Networks via Pinning Control

In this brief, we investigate the cluster synchronization of multi-weighted complex networks with pinning control. We assume that the network contains multiple coupling matrices, and they can be all asymmetric (including the symmetric case), which is more practical in the real world. For multiple asymmetric coupling matrices, the Lyapunov function is hard to design. We firstly define a candidate region for every matrix. Then if these regions are not too far, we can find (at least) a common vector lying in each region. This method has geometrical meaning, so it is different from previous LMI method. That is to say, we can design a new Lyapunov function with a vector combining all normalized left eigenvectors (NLEVec) corresponding to the zero eigenvalue of coupling matrices. With some sufficient conditions presented accordingly, the realization of the cluster synchronization is guaranteed. Especially, we carefully discuss the case with three coupling matrices. The adaptive rule for cluster synchronization is also designed. Finally, numerical simulations are given to demonstrate our results’ effectiveness.