Derived Synchronization Criteria Research Articles

Adaptive control-based synchronization of discrete-time fractional-order fuzzy neural networks with time-varying delays

This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ-difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a novel discrete-time adaptive controller with time-varying delay is designed, by virtue of 1-norm Lyapunov function and newly established lemmas herein as well as inequality techniques and contradiction method, some judgement conditions are derived to guarantee complete synchronization for the explored DFFNNs. Benefitting from discrete-time adaptive control strategy and our analysis method, the conservatism of the derived synchronization criteria is reduced. Ultimately, the effectiveness of our theoretical results and secure communication scheme are demonstrated through two numerical examples.

Synchronization for Complex Networks With Multiple State or Delayed State Couplings Under Recoverable Attacks

In this article, we, respectively, take the synchronization into consideration for directed and undirected complex networks (CNs) with multiple state or delayed state couplings subject to recoverable attacks. By selecting appropriate Lyapunov functional, employing inequality techniques, and adopting the designed state-feedback controller, two criteria of the synchronization are established for the directed CN with multiple state couplings (CNMSCs). Moreover, the synchronization of CNMSCs is also discussed for the case that the network topology is undirected. In addition, two types of CNs with multiple delayed state couplings are also proposed, and several criteria of synchronization are formulated for these networks. Finally, two examples are given to verify the correctness of the derived synchronization criteria.

Quantized control for finite-time synchronization of delayed fractional-order memristive neural networks: The Gronwall inequality approach

This paper is concerned with the finite-time synchronization (FTS) of delayed fractional-order memristive neural networks (FMNNs) by using quantized control. Firstly, two kinds of quantized controllers are designed to eliminate the residual synchronization errors that appear owing to the characteristics of memristive connection weights. Then, to derive α-dependent FTS criteria for drive–response FMNNs, the Gronwall inequality technique is used by combination with the direct estimation method. Compared with the existing results, the advantages of the derived synchronization criteria are discussed from the aspects of both theory and simulation. In addition, the relationships between the finite-time parameter and the quantization parameters are displayed. It reveals that there is a compromise between the admissible finite-time and the saved network bandwidth. Finally, two examples are given to illustrate the effectiveness of the obtained results.

Mittag-Leffler synchronization of fractional-order coupled neural networks with mixed delays

This paper is devoted to investigating Mittag-Leffler synchronization of fractional-order coupled neural networks (FOCNNs) with mixed delays, where the time-varying delays and infinite distributed delays are both taken into account. Firstly, a universal delayed FOCNNs model is introduced, which includes several FOCNNs with various time delays structures such as distributed delays and constant delays or time-varying delays, as its special cases. Besides, for the case where the existing results cannot be applied to infinite time delays, a generalized fractional-order Halanay inequality is proposed, which facilitates the analysis of synchronization of FOCNNs. Based on the generalized inequality, a unified synchronization analysis framework for FOCNNs is established, which is also applied to the cases with commonly considered FOCNNs with distribute delays, constant or time-varying delays. All the derived synchronization criteria have similar results and can be easily verified. Finally, a numerical example is provided to show the effectiveness of obtained results.

Synchronization of the Networked System With Continuous and Impulsive Hybrid Communications.

Many networked systems display some kind of dynamics behaving in a style with both continuous and impulsive communications. The cooperation behaviors of these networked systems with continuous connected or impulsive connected or both connected topologies of communications are important to understand. This paper is devoted to the synchronization of the networked system with continuous and impulsive hybrid communications, where each topology of communication mode is not connected in every moment. Two kind of structures, i.e., fixed structure and switching structures, are taken into consideration. A general concept of directed spanning tree (DST) is proposed to describe the connectivity of the networked system with hybrid communication modes. The suitable Lyapunov functions are constructed to analyze the synchronization stability. It is showed that for fixed topology having a jointly DST, the networked system with continuous and impulsive hybrid communication modes will achieve asymptotic synchronization if the feedback gain matrix and the average impulsive interval are properly selected. The results are then extended to the switching case where the graph has a frequently jointly DST. Some simple examples are then given to illustrate the derived synchronization criteria.

Adaptive Synchronization of Reaction-Diffusion Neural Networks and Its Application to Secure Communication.

This paper is mainly concerned with the synchronization problem of reaction-diffusion neural networks (RDNNs) with delays and its direct application in image secure communications. An adaptive control is designed without a sign function in which the controller gain matrix is a function of time. The synchronization criteria are established for an error model derived from master-slave models through solving the set of linear matrix inequalities derived by constructing the suitable novel Lyapunov-Krasovskii functional candidate, Green's formula, and Wirtinger's inequality. If the proposed sufficient conditions are satisfied, then the global asymptotic synchronization of the error model is guaranteed. The numerical illustrations are provided to demonstrate the validity of the derived synchronization criteria. In addition, the role of system parameters is picturized through the chaotic nature of RDNNs and those unprecedented solutions is utilized to promote better security of image transactions. As is evident, the enhancement of image encryption algorithm is designed with two levels, namely, image watermarking and diffusion process. The contributions of this paper are discussed as concluding remarks.

Outer synchronization between dynamic varying networks under noisy condition

ABSTRACTThis paper exploits the outer synchronization between two dynamic networks with diversely varying node behaviours at the presence of noise. Aiming to obtain a generic technical solution for network outer synchronization, the problem is addressed for the dynamic network scenarios with non-identical topological structures, nonlinear inner coupling connections and time-delayed node characteristics. The impact of noise is fully considered in the theoretical and performance analysis which makes the derived synchronization criteria be able to be adopted in practical engineering deployment with minimized hurdles. By using a Lyapunov–Krasovskii energy function, the synchronization criteria and adaptive control solution are presented and the convergence of the system error states is also proved. Finally, the numerical analysis is carried out based on the simulation study and the result verifies the correctness and effectiveness of the suggested control solution.

Pinning synchronization of complex directed dynamical networks under decentralized adaptive strategy for aperiodically intermittent control

In this paper, the problem of global synchronization for complex directed dynamical networks via adaptive aperiodically intermittent pinning control is studied. By constructing a piecewise Lyapunov function, some sufficient conditions to guarantee global synchronization are derived based on the analytical technique and theory of series with nonnegative terms. Different from previous works, the adaptive intermittent pinning control is aperiodic with non-fixed both control period and control width, and moreover, the adaptive approach is decentralized relying only on the state information of the controlled node. Hence, the adaptive intermittent pinning control strategy proposed in this paper is more practically applicable than those in previous works. Additionally, it is noted that the derived synchronization criteria are dependent on the control rates, but not the control widths or the control periods, which makes the theoretical results are less conservative than the corresponding results given in the existing works. A numerical example is finally provided to illustrate the validity of our theoretical results.

Adaptive synchronization of memristive neural networks with time-varying delays and reaction–diffusion term

This paper focuses on the synchronization control methodology for a class of delayed reaction–diffusion memristor-based neural networks. Adaptive controllers are designed such that the considered model can realize asymptotical and exponential synchronization goal under the framework of inequality techniques and Lyapunov method. The results obtained in this paper consider the effect of time delays as well as the reaction–diffusion terms, which generalize and improve some existing results. The derived synchronization criteria are presented in the form of algebraic, which can be easily verified. Finally, numerical example and its simulations are given to show the correctness of the obtained results.

New synchronization criteria for an array of neural networks with hybrid coupling and time-varying delays

This paper is concerned with the global exponential synchronization for an array of hybrid coupled neural networks with time-varying leakage delay, discrete and distributed delays. Applying a novel Lyapunov functional and the property of outer coupling matrices of the neural networks, sufficient conditions are obtained for the global exponential synchronization of the system. The derived synchronization criteria are closely related with the time-varying delays and the coupling structure of the networks. The maximal allowable upper bounds of the time-varying delays can be obtained guaranteeing the global synchronization for the neural networks. The method we adopt in this paper is different from the commonly used linear matrix inequality (LMI) technique, and our synchronization conditions are new, which are easy to check in comparison with the previously reported LMI-based ones. Some examples are given to show the effectiveness of the obtained theoretical results.

New synchronization criteria for memristor-based networks: Adaptive control and feedback control schemes

In this paper, we investigate synchronization for memristor-based neural networks with time-varying delay via an adaptive and feedback controller. Under the framework of Filippov’s solution and differential inclusion theory, and by using the adaptive control technique and structuring a novel Lyapunov functional, an adaptive updated law was designed, and two synchronization criteria were derived for memristor-based neural networks with time-varying delay. By removing some of the basic literature assumptions, the derived synchronization criteria were found to be more general than those in existing literature. Finally, two simulation examples are provided to illustrate the effectiveness of the theoretical results.

Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency

This paper investigates global synchronization in an array of coupled neural networks with time-varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a novel integral inequality and the Lyapunov functional method, sufficient synchronization criteria are derived. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using Matlab LMI Toolbox. It is displayed that, when some of the transmission efficiencies are limited, the dynamics of the synchronized state are different from those of the isolated node. Furthermore, the transmission efficiency and inner coupling matrices between nodes play important roles in the final synchronized state. The derivative of the time-varying delay can be any given value, and the time-varying delay can be unbounded. The outer-coupling matrices can be symmetric or asymmetric. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.

Synchronization of coupled neural networks with random coupling strengths and mixed probabilistic time‐varying delays

SUMMARYThis paper investigates the global asymptotic synchronization in an array of coupled neural networks with random coupling strengths, probabilistic interval time‐varying coupling delays as well as unbounded distributed delays (mixed delays). Two important integral inequalities that include the Jensen's inequality as a special case are developed. On the basis of the developed inequalities, the properties of random variables and Lyapunov functional method, several delay‐dependent sufficient synchronization criteria are derived for the considered model. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using MATLAB LMI Toolbox. Some existing results are improved and extended by taking different values of parameters of the obtained results. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.