Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.     

Robust stability for stochastic Hopfield neural networks with time delays

In this paper, the asymptotic stability analysis problem is considered for a class of uncertain stochastic neural networks with time delays and parameter uncertainties. The delays are time-invariant, and the uncertainties are norm-bounded that enter into all the network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov–Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be checked readily by using some standard numerical packages, and no tuning of parameters is required. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

Improved asymptotic stability analysis for uncertain delayed state neural networks

This paper presents a new linear matrix inequality (LMI) based approach to the stability analysis of artificial neural networks (ANN) subject to time-delay and polytope-bounded uncertainties in the parameters. The main objective is to propose a less conservative condition to the stability analysis using the Gu’s discretized Lyapunov–Krasovskii functional theory and an alternative strategy to introduce slack matrices. Two computer simulations examples are performed to support the theoretical predictions. Particularly, in the first example, the Hopf bifurcation theory is used to verify the stability of the system when the origin falls into instability. The second example is presented to illustrate how the proposed approach can provide better stability performance when compared to other ones in the literature.     

Stability analysis in Lagrange sense for a non-autonomous Cohen–Grossberg neural network with mixed delays

The paper discusses the global exponential stability in the Lagrange sense for a non-autonomous Cohen–Grossberg neural network (CGNN) with time-varying and distributed delays. The boundedness and global exponential attractivity of non-autonomous CGNN with time-varying and distributed delays are investigated by constructing appropriate Lyapunov-like functions. Moreover, we provide verifiable criteria on the basis of considering three different types of activation function, which include both bounded and unbounded activation functions. These results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. In the end, an illustrative example is given to verify our results.     

A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion

This paper deals with the problem of global exponential stability for bidirectional associate memory (BAM) neural networks with time-varying delays and reaction-diffusion terms. By using some inequality techniques, graph theory as well as Lyapunov stability theory, a systematic method of constructing a global Lyapunov function for BAM neural networks with time-varying delays and reaction-diffusion terms is provided. Furthermore, two different kinds of sufficient principles are derived to guarantee the exponential stability of BAM neural networks. Finally, a numerical example is carried out to demonstrate the effectiveness and applicability of the theoretical results.     

State estimation of neural networks with both time-varying delays and norm-bounded parameter uncertainties via a delay decomposition approach

This paper is concerned with the state estimation problem for neural networks with both time-varying delays and norm-bounded parameter uncertainties. By employing a delay decomposition approach and a convex combination technique, we obtain less conservative delay-dependent stability criteria to guarantee the existence of desired state estimator for the delayed neural networks. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed approach.     

Robust synchronization of impulsively-coupled complex switched networks with parametric uncertainties and time-varying delays

This paper presents a general impulsively-coupled complex switched network (ICCSN) model with parametric uncertainties and multiple Time-varying Delays in both the linear and nonlinear terms. The model is more general than those in the literature in that it contains switching behaviors on nodes and impulsive effects in the whole topology. Robust synchronization of ICCSNs with parametric uncertainties and time-varying delays is investigated. Based on the Lyapunov stability theory, delay-independent synchronization conditions for ICCSNs with uncertainties and delays are obtained. In addition, we consider five special synchronization cases: ICCSNs with delays in both the linear and nonlinear terms, ICCSNs with parametric uncertainties and delays either in the linear or in the nonlinear term, ICCSNs without switching behaviors but with parametric uncertainties and delays, and impulsively-switched-coupled complex switched network with uncertainties and delays. A systematic-design procedure is presented, and a numerical example is carried out to demonstrate the effectiveness of the proposed synchronization strategy. A comparative study of the maximum impulsive intervals for synchronization is presented for all special cases.     

Decentralized feedback control of uncertain cellular neural networks subject to time-varying delays and dead-zone input

This paper investigates the stabilization problem for uncertain cellular neural networks (CNNs) subject to time-varying delays and dead-zone input. On the basis of Lyapunov stability theory, a memoryless decentralized feedback control law is derived for guaranteeing global exponential stability of the system. The main results illustrate that the derived control law does not impose restriction on the derivative of the time-varying delays and can be applied to stabilizing the uncertain CNNs with time-varying delays and dead-zone input. An illustrative example is given to justify the validity and feasibility of the proposed control scheme.     

Global exponential stability of impulsive Cohen–Grossberg neural network with time-varying delays

In this paper, the impulsive Cohen–Grossberg neural network model with time-varying delays is considered. Applying the idea of vector Lyapunov function, M-matrix theory and inequality technique, several new sufficient conditions are obtained to ensure global exponential stability of equilibrium point for impulsive Cohen–Grossberg neural network with time-varying delays. These results generalize a few previous known results and remove some restrictions on the neural network. An example is given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of the Cohen–Grossberg neural network.     

Exponential stability analysis of uncertain stochastic neural networks with multiple delays

This paper addresses the stability analysis problem for stochastic neural networks with parameter uncertainties and multiple time delays. The delays are time varying, and the parameter uncertainties are assumed to be norm bounded. A sufficient condition is derived such that for all admissible uncertainties, the considered neural network is globally exponentially stable in the mean square. The stability criterion is formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily checked in practice. Finally, a numerical example is provided to illustrate the proposed result.     

Exponential stability of hybrid stochastic recurrent neural networks with time-varying delays

In this paper, we consider a class of hybrid Stochastic recurrent neural networks with time-varying delays. By using Razumikhin-type theorem, we not only obtain–almost surely–the exponential stability but also estimate the exponentially convergent rate.     

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.     

Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays

In this paper, the global asymptotic stability is investigated for a class of neutral stochastic neural networks with time-varying delays and norm-bounded uncertainties. Based on Lyapunov stability theory and stochastic analysis approaches, delay-dependent criteria are derived to ensure the global, robust, asymptotic stability of the addressed system in the mean square for all admissible parameter uncertainties. The criteria can be checked easily by the LMI Control Toolbox in Matlab. A numerical example is given to illustrate the feasibility and effectiveness of the results.     

PERIODIC SOLUTIONS AND STABILITY ANALYSIS FOR NEURAL NETWORKS WITH TIME-VARYING DELAY

1 IntroductionIt is well known that both in biological and man-made neural systems, inte-gl.ation afld communication delays are ubiquitous, and often become sources ofinstabilitY' The de1ays in electronic neural networks are usually time varying,and sometimes vary vio1ently with time due to the finite switching speed ofamplifiers and faults in the electrical circuit. They s1ow down the transmissionrate and tend to introduce some degree of instability in circuits. Therefore,fast response must …     

Global existence of periodic solutions in a special neural network model with two delays

A simple neural network model with two delays is considered. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when the sum of two delays passes through a sequence of critical values. Using a global Hopf bifurcation theorem for FDE due to Wu [Wu J. Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc 1998;350:4799–838], a group of sufficient conditions for this model to have multiple periodic solutions are obtained when the sum of delays is sufficiently large. Numerical simulations are presented to support the obtained theoretical results.     

Delay-range dependent stability criteria for neural networks with Markovian jumping parameters

The paper is concerned with a stability analysis problem for neural networks with Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process, which are governed by a Markov process with discrete and finite state space. A new type of Markovian jumping matrix P_i is introduced in this paper. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the lower conservatism and the effectiveness of the proposed LMI conditions.     

非自治变时滞Cohen-Grossberg网络的Lagrange稳定性和全局指数吸引集

基于考虑两种不同类型的激活函数,本文研究了非自治变时滞Cohen-Grossberg神经网络（CGNN）在Lagrange意义下的全局指数稳定性,通过利用新的不等式技巧和构造恰当的Lyapunov泛函给出非自治变时滞CGNN模型在Lagrange意义下全局指数稳定性（即一致有界性）以及对其全局指数吸引集估计的代数判据,并给出应用例子加以验证.     

无界变时滞神经网络全局稳定性

该文研究了具无界变时滞的时变神经网络的全局稳定性.利用两种不同的分析方法得到了保证这类神经网络全局渐近稳定的一些充分条件.推广和改进了现有文献中常时滞或时滞为零的相应结果.     

基于LMI方法的多时滞随机神经网络的指数稳定性

研究了一类具有多个时滞的随机神经网络的均方指数稳定性问题,应用Lyapunov-Krasovskii泛函稳定理论和线性矩阵不等式(LMI)方法,建立了该系统解的指数稳定判别准则,最后通过数值举例阐述了结果的有效性.     

具有变时滞和脉冲效应的Hopfield神经网络的全局指数稳定性

讨论了一类具有变时滞和脉冲效应的Hopfield神经网络模型．利用按段连续的向量Liapunov思想方法,研究了脉冲时滞神经网络的全局指数稳定性．例子及其数值仿真说明了结果的有效性．推广和改进了已有文献的一些结果．