Global Synchronization Problem Research Articles

Pinning synchronization of nonlinearly coupled complex networks with time-varying delays using M-matrix strategies

In this paper, we investigate the global synchronization problem for a class of nonlinearly-coupled complex networks (NCCNs) with mixed time-varying delays by using an M-matrix approach. The M-matrix strategy allows many synchronization problems with much relaxed conditions to be considered and can be used to derive sufficient conditions for this new class of NCCNs by pinning control. We also propose an effective way of adapting the coupling strengths of complex networks and give numerical examples to illustrate the effectiveness of our theoretical results.

Impulsive stabilization and synchronization of Hopfield-type neural networks with impulse time window

This paper studies the problem of global exponential stabilization and synchronization for impulsive Hopfield-type neural networks with impulse time window. By using the stability theory of impulsive dynamical systems, some sufficient conditions guaranteeing the global exponential stabilization and synchronization of Hopfield-type NNs are derived. The main innovation embodies that the impulsive instants are no longer limited at fixed instants, but suggested to be at some certain time intervals, named by impulse time windows. We shall show that impulses occurring randomly in impulse time windows can still stabilize and/or synchronize the considered neural networks under certain suitable assumptions. Two numerical examples are also given to illustrate the effectiveness of theoretical results.

Sampled-data synchronization of randomly coupled reaction–diffusion neural networks with Markovian jumping and mixed delays using multiple integral approach

This paper is devoted to investigate the problem of global asymptotic synchronization of an array of N randomly coupled reaction---diffusion neural networks with Markovian jumping parameters and mixed delays using sampled-data control technique. The jump parameters are determined by a continuous-time, discrete-state Markovian chain, and the mixed time delays under consideration comprise both discrete and distributed delays. A multiple integral inequality is proposed firstly in Markovian jump reaction---diffusion neural networks with mixed delays. Through constructing appropriate Lyapunov---Krasovskii functional including multiple integral terms, some novel synchronization criteria in terms of linear matrix inequalities are derived. The obtained LMIs can be easily verified for feasibility through any of the available softwares. Finally, numerical examples with simulations are provided to illustrate the effectiveness of the proposed theoretical results.

Lag Synchronization of Switched Neural Networks via Neural Activation Function and Applications in Image Encryption.

This paper investigates the problem of global exponential lag synchronization of a class of switched neural networks with time-varying delays via neural activation function and applications in image encryption. The controller is dependent on the output of the system in the case of packed circuits, since it is hard to measure the inner state of the circuits. Thus, it is critical to design the controller based on the neuron activation function. Comparing the results, in this paper, with the existing ones shows that we improve and generalize the results derived in the previous literature. Several examples are also given to illustrate the effectiveness and potential applications in image encryption.

Synchronization of switched complex dynamical networks with non-synchronized subnetworks and stochastic disturbances

In this paper, the global synchronization problem of switched complex dynamical networks (SCDNs) with stochastic disturbances is investigated. Different from the existing results concerning synchronization of switched complex networks, all the subnetworks of the SCDNs here are not self-synchronized. Based on the dwell time approach and the discretized Lyapunov function technique, a sufficient synchronization criterion is obtained in term of linear matrix inequalities (LMIs) and the corresponding switching signal is obtained. The obtained switching signal depends on time rather than the system states, which makes it easier to be implemented. Finally, two examples are provided to illustrate the effectiveness of the theoretical results.

Decomposition approach to exponential synchronisation for a class of non‐linear singularly perturbed complex networks

This study is concerned with the globally exponential synchronisation problem for a class of non-linear singularly perturbed complex networks where all nodes possess the same structure and properties. The addressed global synchronisation problem is converted into the one for two lower-order sub-networks, namely, a non-linear slow sub-network and a linear fast sub-network, which are obtained by using the classical singular perturbation decomposition method. The network topology is directed and weighted, which means that the coupling configuration matrix is allowed to be asymmetric. By using the Lyapunov functional method and the Kronecker product technique, sufficient conditions are obtained under which the synchronisation is achieved, respectively, for the two sub-networks and the original complex network. These conditions can be easily verified by using the semi-definite programming method. A numerical example is finally simulated to validate the theoretical results and the effectiveness of the proposed synchronisation scheme.

Synchronization of complex dynamical networks with discrete time delays on time scales

This paper investigates the global exponential synchronization problem in arrays of complex networks with time delays based on the theory of calculus on time scales, Lyapunov functional and linear matrix inequality technique, and derives several sufficient criteria to ensure the global exponential synchronization for the considered networks. It is shown that the synchronization conditions of complex dynamical networks on time scales are different from those derived for conventional continuous or discrete complex networks. Moreover, the presented results of this paper indicate that the globally synchronization problems with both discrete time case and continuous time case can be addressed in a unified framework.

Improved stability criteria for synchronization of chaotic Lur׳e systems using sampled-data control

The problem of global asymptotical synchronization of chaotic Lur׳e systems using sampled-data controller is considered in this paper. The new method is based on a novel construction of piecewise differentiable Lyapunov–Krasovskii functional (LKF) in the framework of an input delay method. Compared with existing works, the new LKF makes full use of the information in the nonlinear part of the system and introduces the novel terms, which guarantees the positive of the whole LKF. The obtained stability condition is less conservative than some of the existing ones. A longer sampling period is achieved with the new method. The numerical examples are given and the simulations are performed on Chua׳s circuit. The results show the superiorities and effectiveness of the proposed method.

Global synchronization for a class of Markovian switching complex networks with mixed time-varying delays in the delay-partition approach

Abstract In this paper, global synchronization problem for a class of Markovian switching complex networks (MSCNs) with mixed time-varying delays under the delay-partition approach is investigated. A novel delay-partition approach is developed to derive sufficient conditions for a new class of MSCNs with mixed time-varying delays. The proposed delay-partition approach can give global synchronization results lower conservatism. Two numerical examples are provided to illustrate the effectiveness of the theoretical results.

Synchronization of a class of uncertain stochastic discrete-time delayed neural networks

Abstract The global asymptotical synchronization problem is discussed for a general class of uncertain stochastic discrete-time neural networks with time delay in this paper. Time delays include time-varying delay and distributed delay. Based on the drive-response concept and the Lyapunov stability theorem, a linear matrix inequality (LMI) approach is given to establish sufficient conditions under which the considered neural networks are globally asymptotically synchronized in the mean square. Therefore, the global asymptotical synchronization of the stochastic discrete-time neural networks can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Moreover, the obtained results are dependent not only on the lower bound but also on the upper bound of the time-varying delays, that is, they are delay-dependent. And finally, a simulation example is given to illustrate the effectiveness of the proposed synchronization scheme.

Global chaos synchronization of new chaotic system using linear active control

Chaos synchronization is a procedure where one chaotic oscillator is forced to adjust the properties of another chaotic oscillator for all future states. This research paper studies and investigates the global chaos synchronization problem of two identical chaotic systems and two non‐identical chaotic systems using the linear active control technique. Based on the Lyapunov stability theory and using the linear active control technique, the stabilizing controllers are designed for asymptotically global stability of the closed‐loop system for both identical and non‐identical synchronization. Numerical simulations and graphs are imparted to justify the efficiency and effectiveness of the proposed scheme. All simulations have been done by using mathematica 9. © 2014 Wiley Periodicals, Inc. Complexity 21: 379–386, 2015

Intermittent control on switched networks via $${\varvec{\omega }}$$ ω -matrix measure method

This paper is concerned with global exponential synchronization problem for a class of switched delay networks with interval parameters uncertainty, different from the most existing results, without constructing complex Lyapunov–Krasovskii functions; \(\omega \)-matrix measure method is firstly introduced to switched interval networks, combining Halanay inequality technique, designing proper intermittent and non-intermittent control strategy; some easy-to-verify synchronization criteria are given to ensure the global exponential synchronization of switched interval networks under arbitrary switching rule and for admissible interval uncertainties. Moreover, as an application, the proposed scheme can be applied to chaotic neural networks. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results and show the obtained results via employing \(\omega \)-measure are superior to previous results by using \(1\)-measure.

Global exponential synchronization of nonlinear time-delay Lur’e systems via delayed impulsive control

This paper is concerned with the global exponential synchronization problem of two identical nonlinear time-delay Lur’e systems via delayed impulsive control. Some novel impulsive synchronization criteria are obtained by introducing a discontinuous Lyapunov function and by using the Lyapunov–Razumikhin technique, which are expressed in forms of linear matrix inequalities. The derived criteria reveal the effects of impulsive input delays and impulsive intervals on the stability of synchronization error systems. Then, sufficient conditions on the existence of a delayed impulsive controller are derived by employing these newly-obtained synchronization criteria. Additionally, some synchronization criteria for two identical time-delay Lur’e systems with impulsive effects are presented by using delayed continuous feedback control. The synchronization criteria via delayed continuous feedback control can deal with the case when the impulsive control strategy fails to synchronize two identical impulsive time-delay Lur’e systems. Three numerical examples are provided to illustrate the efficiency of the obtained results.

Exponential synchronization of memristive Cohen-Grossberg neural networks with mixed delays.

This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The drive-response set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen-Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen-Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristor-based neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.

Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays

This paper deals with the problem of global exponential synchronization of a class of memristor-based recurrent neural networks with time-varying delays based on the fuzzy theory and Lyapunov method. First, a memristor-based recurrent neural network is designed. Then, considering the state-dependent properties of the memristor, a new fuzzy model employing parallel distributed compensation (PDC) gives a new way to analyze the complicated memristor-based neural networks with only two subsystems. Comparisons between results in this paper and in the previous ones have been made. They show that the results in this paper improve and generalized the results derived in the previous literature. An example is also given to illustrate the effectiveness of the results.

Global Exponential Adaptive Synchronization of Complex Dynamical Networks With Neutral-Type Neural Network Nodes and Stochastic Disturbances

This paper is on the design problem of global exponential adaptive synchronization for a class of stochastic complex dynamical networks. In the considered networks, the dynamics of each node are approximated by a neutral-type neural network. The stochastic disturbances are described in terms of Brownian motions. Different from the prior references, the coefficient matrix of the adaptive controller under consideration is an arbitrary matrix instead of an identity one. By using Lyapunov method and some properties of Kronecker product, a sufficient condition is proposed to ensure the dynamics of the considered network globally exponentially synchronize with the desired solution in the mean square sense. Some criteria for global exponential adaptive synchronization of complex dynamical networks with general nodes are further provided in forms of corollaries. In particular, the proposed criteria for network synchronization are in terms of linear matrix inequalities. Only two variables are used in each criterion and the variables are not inside of any Kronecker product. Hence, the conditions are easy to check. A numerical example is presented to show the effectiveness and applicability of the proposed approach.

Outer Synchronization between Fractional-Order Complex Networks: A Non-Fragile Observer-based Control Scheme

This paper addresses the global outer synchronization problem between two fractional-order complex networks coupled in a drive-response configuration. In particular, for a given fractional-order complex network composed of Lur’e systems, an observer-type response network with non-fragile output feedback controllers is constructed. Both additive and multiplicative uncertainties that perturb the control gain matrices are considered. Then, using the stability theory of fractional-order systems and eigenvalue distribution of the Kronecker sum of matrices, we establish some sufficient conditions for global outer synchronization. Interestingly, the developed results are cast in the format of linear matrix inequalities (LMIs), which can be efficiently solved via the MATLAB LMI Control Toolbox. Finally, numerical simulations on fractional-order networks with nearest-neighbor and small-world topologies are given to support the theoretical analysis.

GLOBAL SYNCHRONIZATION OF MULTI-SCROLL SATURATED CHAOTIC SYSTEMS VIA SINGLE-STATE LINEAR FEEDBACK CONTROL

This paper investigates the global synchronization problem of master–slave coupled multi-scroll saturated chaotic systems via single-state linear feedback control. An algebraic criterion for global synchronization is rigorously proven by means of the absolute stability theory. The obtained algebraic criterion is then optimized thereby deriving a less-conservative result, which is finally verified by numerical examples.

The Synchronization Problem on a Class of Supply Chain Complex Network

we investigate the global adaptive synchronization problem for a class of supply chain complex networks that have nonlinearly coupled identical nodes and an asymmetrical coupling matrix. We derive, in particular, a sufficient condition for global synchronization when the coupling strength is not excessively large by applying a suitably chosen adaptive controller and demonstrate the effectiveness of this theory by numerical examples.

Global asymptotical synchronization of delayed complex dynamical networks with switching topology

In this paper, we study the global asymptotical synchronization problem of delayed complex dynamical networks with a pre-given collection of general connection topologies where synchronization cannot be achieved by using any topology alone in this collection. By using single Lyapunov and multiple Lyapunov function methods, two global asymptotical synchronization conditions with the design of switching within the pre-given collection of topologies are presented for synchronizing such complex dynamical networks. According to the topological structure of the connection matrices, we consider more general forms. Simultaneous triangularizability, diagonalizability or even symmetry of the connection matrices is no longer assumed. Finally, simulation results are used to demonstrate the effectiveness of the proposed results.