Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays

This paper considers the chaotic synchronization problem of neural networks with time-varying and distributed delays using impulsive control method. By utilizing the stability theory for impulsive functional differential equations, several impulsive control laws are derived to guarantee the exponential synchronization of neural networks with time-varying and distributed delays. It is shown that chaotic synchronization of the networks is heavily dependent on the designed impulsive controllers. Moreover, these conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. Finally, a numerical example and its simulation are given to show the effectiveness and advantage of the proposed control schemes.     

Synchronization of chaotic neural networks with mixed time delays

In this paper, we investigate the synchronization problems of chaotic neural networks with mixed time delays. We first establish the sufficient conditions for synchronization of identical chaotic neural networks with mixed time delays via linear output feedback control. To overcome the difficulty that complete synchronization between nonidentical chaotic neural networks cannot be achieved only by utilizing output feedback control, we use a sliding mode control approach to study the synchronization of nonidentical chaotic neural networks with mixed time delays, where the parameters and functions are mismatched. Numerical simulations are carried out to illustrate the main results.     

Analysis of global exponential stability and periodic solutions of FCNNs with constant delays and time-varying delays

In this paper, we investigate a class of fuzzy cellular neural networks with constant delays and time-varying delays. By constructing suitable Lyapunov functional and employing Young inequality, we find sufficient conditions for the existence, uniqueness, global exponential stability of equilibrium, and the existence of periodic solutions of fuzzy cellular neural networks with time-varying delays. The results of this paper are new and they extend previously known results.     

Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction-diffusion

Separate studies have been published on the stability of fuzzy cellular neural networks with time delay in the leakage term and synchronization issue of coupled chaotic neural networks with stochastic perturbation and reaction-diffusion effects. However, there have not been studies that integrate the two fields. Motivated by the achievements from both fields, this paper considers the exponential synchronization problem of coupled chaotic fuzzy cellular neural networks with stochastic noise perturbation, time delay in the leakage term and reaction-diffusion effects using linear feedback control. Lyapunov stability theory combining with stochastic analysis approaches are employed to derive sufficient criteria ensuring the coupled chaotic fuzzy neural networks to be exponentially synchronized. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.     

Synchronization schemes for coupled identical Yang–Yang type fuzzy cellular neural networks

This paper proposes an adaptive procedure to the problem of synchronization for a class of coupled identical Yang–Yang type fuzzy cellular neural networks (YYFCNN) with time-varying delays. Based on the simple adaptive controller, a set of sufficient conditions are developed to guarantee the synchronization of the coupled YYFCNN with time-varying delays. The results are much different from previous ones. It is proved that two coupled identical YYFCNN with time-varying delays can achieve synchronization by enhancing the coupled strength dynamically. In addition, this kind of controller is simple to be implemented and it is fairly robust against the effect of weak noise in the given time series. The approaches are based on using the invariance principle of functional differential equations, constructing a general Lyapunov–Krasovskii functional and employing a linear matrix inequality (LMI). An illustrative example and its simulations show the feasibility of our results. Finally, an application is given to show how to apply the presented synchronization scheme of YYFCNN to secure communication.     

Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations

In this paper, we study the exponential synchronization problem of a class of chaotic delayed neural networks with impulsive and stochastic perturbations. The involved time delays include time-varying delays and unbounded distributed delays. Employing the method of impulsive delay differential inequality, several new sufficient conditions ensuring the exponential synchronization are obtained, which can be easily checked by LMI Control Toolbox in Matlab. Compared with the previous methods, our method does not resort to complicated Lyapunov–Krasovkii, and the results derived are independent of the time-varying delays and do not require the differentiability of delay functions and the monotony of the activation functions. Finally, a numerical example and its simulation is given to show the effectiveness of the obtained results in this paper.     

Master-slave synchronization of neural networks with time-varying delays via the event-triggered control

ABSTRACT

This paper investigates the problem of master-slave synchronization of neural networks with time-varying delays via the event-triggered control (ETC). First, the proposed ETC can effectively reduce the total amount of data transmitted to the controller in the synchronization process and avoid communication channel congestion. Second, a master-slave synchronization of neural networks with time-varying delays is constructed, where delays within neural networks and the ETC are simultaneous existence. The controller is updated by the ETC. By the Lyapunov stability theory, some sufficient criteria are obtained to ensure master-slave synchronization of neural networks. Finally, a numerical example and a tunnel diode circuit example are used to verify the validity of results obtained.     

Dynamics of fuzzy impulsive bidirectional associative memory neural networks with time-varying delays

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication

This paper investigates drive-response synchronization of chaotic systems with discontinuous right-hand side. Firstly, a general model is proposed to describe most of known discontinuous chaotic system with or without time-varying delay. An uniform impulsive controller with multiple unknown time-varying delays is designed such that the response system can be globally exponentially synchronized with the drive system. By utilizing a new lemma on impulsive differential inequality and the Lyapunov functional method, several synchronization criteria are obtained through rigorous mathematical proofs. Results of this paper are universal and can be applied to continuous chaotic systems. Moreover, numerical examples including discontinuous chaotic Chen system, memristor-based Chua’s circuit, and neural networks with discontinuous activations are given to verify the effectiveness of the theoretical results. Application of the obtained results to secure communication is also demonstrated in this paper.     

Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling

In this paper, the global exponential synchronization is investigated for an array of asymmetric neural networks with time-varying delays and nonlinear coupling, assuming neither the differentiability for time-varying delays nor the symmetry for the inner coupling matrices. By employing a new Lyapunov-Krasovskii functional, applying the theory of Kronecker product of matrices and the technique of linear matrix inequality (LMI), a delay-dependent sufficient condition in LMIs form for checking global exponential synchronization is obtained. The proposed result generalizes and improves the earlier publications. An example with chaotic nodes is given to show the effectiveness of the obtained result.     

Adaptive synchronization of Cohen-Grossberg neural networks with unknown parameters and mixed time-varying delays

In this paper, we investigate the synchronization problem of chaotic Cohen-Grossberg neural networks with unknown parameters and mixed time-varying delays. An adaptive linear feedback controller is designed to guarantee that the response system can be synchronized with a drive system by utilizing Lyapunov stability theory and parameter identification. Our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. These results generalize a few previous known results and remove some restrictions on amplification function and time delay. This research also demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.     

Synchronization of neural networks based on parameter identification and via output or state coupling

For neural networks with all the parameters unknown, we focus on the global robust synchronization between two coupled neural networks with time-varying delay that are linearly and unidirectionally coupled. First, we use Lyapunov functionals to establish general theoretical conditions for designing the coupling matrix. Neither symmetry nor negative (positive) definiteness of the coupling matrix are required; under less restrictive conditions, the two coupled chaotic neural networks can achieve global robust synchronization regardless of their initial states. Second, by employing the invariance principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the robust synchronization of almost all kinds of coupled neural networks with time-varying delay based on the parameter identification of uncertain delayed neural networks. Finally, numerical simulations validate the effectiveness and feasibility of the proposed technique.     

Stochastic exponential synchronization of jumping chaotic neural networks with mixed delays

This paper deals with the exponential synchronization problem for a class of stochastic jumping chaotic neural networks with mixed delays and sector bounded nonlinearities. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time delays. By applying the Finsler’s Lemma and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent feedback controllers with sector nonlinearities are developed to achieve the synchronization in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve no free weighting matrices, the computational burden is largely reduced. One numerical example is provided to demonstrate the effectiveness of the theoretical results.     

Synchronization of Takagi–Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays

In this paper, we propose and investigate a new general model of fuzzy stochastic discrete-time complex networks (SDCNs) described by Takagi–Sugeno (T–S) fuzzy model with discrete and distributed time-varying delays. The proposed model takes some well-studied models as special cases. By employing a new Lyapunov functional candidate, we utilize some stochastic analysis techniques and Kronecker product to deduce delay-dependent synchronization criteria that ensure the mean-square synchronization of the proposed T–S fuzzy SDCNs with mixed time-varying delays. These sufficient conditions are computationally efficient as it can be solved numerically by the LMI toolbox in Matlab. A numerical simulation example is provided to verify the effectiveness and the applicability of the proposed approach.     

Stability analysis of Takagi–Sugeno fuzzy Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays

In this paper, the global asymptotic stability problem of Takagi–Sugeno (TS) fuzzy Cohen–Grossberg Bidirectional Associative Memory neural networks (FCGBAMNNs) with discrete and distributed time-varying delays is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of FCGBAMNNs which are represented by TS fuzzy models. Our results can be easily verified and are also less restrictive than previously known criteria and can be applied to Cohen–Grossberg neural networks, recurrent neural networks and cellular neural networks. Finally, the proposed stability conditions are demonstrated with a numerical example.     

Chaotic synchronization of a fractional-order system based on washout filter control

In this paper, chaos in a fractional-order neural network system with varying time delays is presented, and chaotic synchronization system with varying time delays is constructed. The stability of constructed synchronization system is analyzed by Laplace transformation theory. In addition, the bifurcation graph of the chaotic system is illustrated. The study results show that the chaos in such fractional-order neural networks with varying time delay can be synchronized, and Washout filter control can be used to reduce the range of coupled parameter.     

Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays

This paper is concerned with the adaptive synchronization problem for a class of stochastic delayed neural networks. Based on the LaSalle invariant principle of stochastic differential delay equations and the stochastic analysis theory as well as the adaptive feedback control technique, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving complete synchronization of unidirectionally coupled stochastic delayed neural networks. In particular, the synchronization criterion considered in this paper is the globally almost surely asymptotic stability of the error dynamical system, which has seldom been applied to investigate the synchronization problem. Moreover, the delays proposed in this paper are time-varying delays and distributed delays, which have rarely been used to study the synchronization problem for coupled stochastic delayed neural networks. Therefore, the results obtained in this paper are more general and useful than those given in the previous literature. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the theoretical results.     

Synchronization of switched neural networks with mixed delays via impulsive control

This paper concerns the problem of global exponential synchronization for a class of switched neural networks with time-varying delays and unbounded distributed delays via impulsive control method. By using Lyapunov stability theory, new synchronization criterion is derived. In our synchronization criterion, the switching law can be arbitrary and the concept of average impulsive interval is utilized such that the obtained synchronization criterion is less conservative than those based on maximum of impulsive intervals. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical results.     

随机变时滞模糊神经网络的均方指数稳定性

利用Lyapunov泛函和随机分析的方法,研究了一类具有变时滞随机模糊细胞神经网络的均方指数稳定性,得到了这类神经网络均方指数稳定性的充分条件.数值例子说明了得到的结果的有效性.     

Global synchronization of weighted cellular neural network with time-varying coupling delays

New sufficient conditions are derived to guarantee the global synchronization of the weighted cellular neural network with multiple time delays. Based on Lyapunov theory, this paper proposes an adaptive feedback controlling method to identify the exact topology of a rather general weighted cellular neural network system with time-varying delays and then considers the synchronization of the neural network with different nodes dynamics. The parameters in this paper are very few and experiments show that the methods presented in this paper are of high application in global synchronization.