Synchronization Of Complex Dynamical Networks Research Articles

Finite-time synchronization of complex dynamical networks with multi-links via intermittent controls

This paper considers finite-time synchronization of complex multi-links dynamical networks with or without internal time delays via intermittent controls. Two simple intermittent feedback controllers are designed to achieve finite-time synchronization between the drive and response system. Some novel and effective finite-time synchronization criteria are derived based on finite-time stability analysis techniques. By constructing suitable Lyapunov functions, we theoretically prove its correctness. Finally, two numerical simulation examples are given to show the effectiveness of proposed method in this paper.

Synchronization of complex dynamical networks with uncertain inner coupling and successive delays based on passivity theory

This paper is discussed with the problem of passivity based synchronization for a class of complex dynamical networks (CDNs) consisting uncertain inner coupling matrix together with successive time-varying delays via a state feedback delayed controller. Due to occurrence of uncertainties in coupling strengths, the considered CDNs take account of an uncertain inner coupling strength which is more general than the previously existing inner coupling strengths. Specifically, the uncertainties encountering in coupling terms are characterized with the aid of interval matrix approach. Also, by introducing a simple linear transformation, the corresponding error system is formulated. Then, based on the information about control delay term, two cases are considered namely, differentiable and non-differentiable. More precisely, by constructing an appropriate Lyapunov–Krasovskii functional (LKF) containing triple integral terms in respect of Kronecker product, for both the cases, some sufficient criteria are established in terms of linear matrix inequalities (LMIs) to guarantee the robust synchronization of the addressed CDNs based on passivity property. And the established criteria optimistically reduce the L2 gain level from the disturbance to the output vector. Subsequently, the desired state feedback gain matrix is designed in terms of the solution to a convex optimization problem. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed theoretical results.

Function projective synchronization in complex dynamical networks with or without external disturbances via error feedback control

This paper investigates function projective synchronization (FPS) of complex dynamical networks (CDNs) with or without external disturbances using error feedback control scheme. The proposed error feedback control scheme contains only error terms, which is quite simple and easy to implement in practical applications. Then, an adaptive error feedback control scheme is designed to achieve FPS in CDNs with or without external disturbances, in which feedback gains can be automatically adapted to suitable constants. Moreover, there is no need to know the norm-bounded of the disturbances. Numerical examples are provided to show the effectiveness of proposed methods.

Synchronization of complex dynamical network with piecewise constant argument of generalized type

This paper studies synchronization problems of complex dynamical network with mixed coupling via impulsive control. The model involves both advanced and delayed arguments, and the problem of the existence of the model is analyzed. Based on the stability theory for impulsive differential equations, an effective impulsive control scheme is proposed to achieve synchronization for complex dynamical networks. Finally, an example with numerical simulations is given to illustrate our results.

Controlled synchronization for complex dynamical networks with random delayed information exchanges: A non-fragile approach

This paper studies the controlled synchronization problem for complex dynamical networks based on a non-fragile approach with randomly occurring controller gain fluctuations. In particular, delayed information exchanges among the dynamical nodes are considered, where stochastic variables are utilized to model the randomly occurring phenomena. By constructing the Lyapunov–Krasovskii function, delay-dependent conditions are first derived to achieve the synchronization. Then, the non-fragile feedback synchronization controllers are further designed in terms of the resulting conditions. The effectiveness of the obtained theoretical results is demonstrated by an illustrative example.

Distributed adaptive control of pinning synchronization in complex dynamical networks with non-delayed and delayed coupling

This paper discusses the distributed adaptive control schemes for pinning synchronization in complex dynamical network with non-delayed and delayed coupling. An effective distributed adaptive strategy to adjust simultaneously coupling strength and feedback gains is designed based on information of the non-delayed network’s configuration. For a special case where the information of delay is available, a distributed adaptive scheme to tune the coupling weights of non-delayed coupling network is proposed by using the delayed feedback controllers. Based on the small-world network and scalefree network, simulation examples are given to demonstrate the effectiveness of theoretical analysis.

Distributed adaptive synchronization of complex dynamical network with unknown time-varying weights

A new approach of adaptive distributed control is proposed for a class of networks with unknown time-varying coupling weights. The proposed approach ensures that the complex dynamical networks achieve asymptotical synchronization and all the closed-loop signals are bounded. Furthermore, the coupling matrix is not assumed to be symmetric or irreducible and asymptotical synchronization can be achieved even when the graph of network is not connected. Finally, a simulation example shows the feasibility and effectiveness of the approach.

Formula omitted] synchronization for complex dynamical networks with coupling delays using distributed impulsive control

The H∞ synchronization problem for complex dynamical networks with coupling delays and external disturbance via distributed impulsive control is studied. Two types of time-varying coupling delays are considered: the delays without any restriction on the delay derivatives, and the delays whose derivatives are strictly less than 1. A time-varying Lyapunov function/functional approach is applied to L2-gain analysis of the synchronization error systems. H∞ synchronization criteria are established to guarantee the synchronization to be robust with respect to disturbance in the sense that the L2-gain from the disturbance to the control output is satisfactorily small. For each type of coupling delays, an algorithm involving convex optimization is proposed to design distributed impulsive controllers achieving a suboptimal value of the sum of coupling strengths for a prescribed L2-gain. Two numerical examples illustrate the efficiency of the theoretical results.

Adaptive cluster general projective synchronization of complex dynamic networks in finite time

This paper investigates adaptive cluster general projective synchronization (CGPS) of complex dynamic networks in finite time. Based on the finite time synchronization control techniques and Lyapunov stability theorem, sufficient conditions are derived to guarantee the realization of adaptive cluster general projective synchronization. Finally, numerical simulation is provided to support the theoretical results.

Function projective synchronization between two different complex networks with correlated random disturbances**Project supported by the National Natural Science Foundation of China (Grant No. 61273015).

Although function projective synchronization in complex dynamical networks has been extensively studied in the literature, few papers deal with the problem between two different complex networks with correlated random disturbances. In this paper, we present some novel techniques to analyze the problem of synchronization. A probability approach is introduced to obtain an almost sure synchronization criterion. We also present some efficient approaches to analyze the problem of exponential synchronization. For the problem of synchronization in some complex networks, our approaches not only can replace the LaSalle-type theorem but also allow improvements of existing results in the literature. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approaches.

Mixed [formula omitted]/passive synchronization for complex dynamical networks with sampled-data control

This paper deals with the problem of mixed H∞/passive synchronization for complex dynamical networks (CDNs) with time-varying delayed couplings via a sampled-data control scheme. The purpose is focus on designing controller such that the resulting synchronization error system is stable and a mixed H∞/passive performance level is satisfied. By using some new tools to deal with the Lyapunov functional, a sufficient condition which ensures the existence of the desired controller is presented. Based on the condition, an explicit expression for the desired controller is given. Finally, two examples are employed to demonstrate the effectiveness and the reduced conservatism of the proposed method.

Improved results on sampled-data synchronization of complex dynamical networks with time-varying coupling delay

This paper investigates the problem of synchronization of complex dynamical networks (CDNs) with time-varying coupling delay by using sampled-data control. A synchronization criterion for CDNs is proposed by constructing a suitable Lyapunov–Krasovskii function, and less conservative conditions are formulated in form of linear matrix inequalities by utilizing reciprocally convex approach and integral inequality. Simulation examples are given to demonstrate the effectiveness of the proposed design method.

Synchronization in complex dynamical networks coupled with complex chaotic system

This paper investigates synchronization in complex dynamical networks with time delay and perturbation. The node of complex dynamical networks is composed of complex chaotic system. A complex feedback controller is designed to realize different component of complex state variable synchronize up to different scaling complex function when complex dynamical networks realize synchronization. The synchronization scaling function is changed from real field to complex field. Synchronization in complex dynamical networks with constant delay and time-varying coupling delay are investigated, respectively. Numerical simulations show the effectiveness of the proposed method.

Function projective synchronization in complex networks with switching topology and stochastic effects

Although function projective synchronization in complex dynamical networks has come into the limelight in recent years, litter research has been published on the problem in the dynamical networks with switching topology and stochastic effects. This study aims to fill the gap. In this paper, the problem of function projective synchronization is investigated for complex networks with switching topology and stochastic effects. A hybrid feedback control method is designed to achieve function projective synchronization for the complex network. Using the property of martingale and Gronwally’ inequality, we obtain some conditions to guarantee that the complex network can realize mean square synchronization and mean square exponential synchronization, respectively. Furthermore, we also present a probability approach to the method of Lyapunov functionals to analyze function projective synchronization in the dynamical network under a particular assumption. Our approaches not only can replace the LaSalle-type theorem but also allow improvements of existing results in the literature. In particular, the study also presents an equivalent way of regarding Itô’ integral, which may be a useful tool to deal with the problem of synchronization in variety of complex dynamical networks with stochastic effects. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov–Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen’s inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen’s inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods.

Exponential synchronization of complex networks of linear systems and nonlinear oscillators: a unified analysis.

A unified approach to the analysis of synchronization for complex dynamical networks, i.e., networks of partial-state coupled linear systems and networks of full-state coupled nonlinear oscillators, is introduced. It is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks, thus making it feasible to consider the error dynamics for the whole network system. Different from the other various methods given in the existing literature, the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form, but also explicitly specifying the convergence rate.

Global synchronization of complex dynamical networks through digital communication with limited data rate.

This paper studies the global synchronization of complex dynamical network (CDN) under digital communication with limited bandwidth. To realize the digital communication, the so-called uniform-quantizer-sets are introduced to quantize the states of nodes, which are then encoded and decoded by newly designed encoders and decoders. To meet the requirement of the bandwidth constraint, a scaling function is utilized to guarantee the quantizers having bounded inputs and thus achieving bounded real-time quantization levels. Moreover, a new type of vector norm is introduced to simplify the expression of the bandwidth limit. Through mathematical induction, a sufficient condition is derived to ensure global synchronization of the CDNs. The lower bound on the sum of the real-time quantization levels is analyzed for different cases. Optimization method is employed to relax the requirements on the network topology and to determine the minimum of such lower bound for each case, respectively. Simulation examples are also presented to illustrate the established results.

Synchronization for complex dynamical networks with time delay and discrete-time information

The synchronization problem is studied for complex dynamical networks (CDNs) with time delay based on discrete-time communication pattern. A new Lyapunov functional is proposed, which is positive definite at communication instants but not necessarily positive definite inside the communication intervals, and can make full use of the available information about the discrete-time communication pattern. Based on the Lyapunov functional, an exponential synchronization criterion is proposed to ensure the synchronization of the considered CDNs. The effectiveness of the developed results are shown by the numerical simulation.

Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks

This paper presents a new framework for synchronization of complex network by introducing a mechanism of event-triggering distributed sampling information. A kind of event which avoids continuous communication between neighboring nodes is designed to drive the controller update of each node. The advantage of the event-triggering strategy is the significant decrease of the number of controller updates for synchronization task of complex networks involving embedded microprocessors with limited on-board resources. To describe the system’s ability reaching synchronization, a concept about generalized algebraic connectivity is introduced for strongly connected networks and then extended to the strongly connected components of the directed network containing a directed spanning tree. Two sufficient conditions are presented to reveal the underlying relationships of corresponding parameters to reach global synchronization based on algebraic graph, matrix theory and Lyapunov control method. A positive lower bound for inter-event times is derived to guarantee the absence of Zeno behavior. Finally, a numerical simulation example is provided to demonstrate the theoretical results.

Synchronization of fractional order complex dynamical networks

In this letter the synchronization of complex dynamical networks with fractional order chaotic nodes is studied. A fractional order controller for synchronization of complex network is presented. Some new sufficient synchronization criteria are proposed based on the Lyapunov stability theory and the LaSalle invariance principle. These synchronization criteria can apply to an arbitrary fractional order complex network in which the coupling-configuration matrix and the inner-coupling matrix are not assumed to be symmetric or irreducible. It means that this method is more general and effective. Numerical simulations of two fractional order complex networks demonstrate the universality and the effectiveness of the proposed method.