具分布参数的随机Hopfield神经网络的指数稳定

基于随机Fubini定理,将随机偏微分方程描述的Hopfield神经网络系统转化为用相应的随机常微分方程来描述.利用关于空间变量平均的Lyapunov函数与Ito^公式,通过对所构造的Lyapunov函数在Ito^微分规则下对相应系统求导的方法,获得了系统指数稳定的代数判据及其Lyapunov指数估计.实现了运用Lyapunov直接法对分布参数系统稳定性的研究.     

Ultimate boundedness of stochastic Hopfield neural networks with time-varying delays

By employing Lyapunov functional theory as well as linear matrix inequalities, ultimate boundedness of stochastic Hopfield neural networks (HNN) with time-varying delays is investigated. Sufficient criteria on ultimate boundedness of stochastic HNN are firstly obtained, which fills up a gap and includes deterministic systems as our special case. Finally, numerical simulations are presented to illustrate the correctness and effectiveness of our theoretical results.     

Stochastic stability of Markovian jumping Hopfield neural networks with constant and distributed delays

This paper investigates the problem of stability analysis for Markovian jumping Hopfield neural networks (MJHNNs) with constant and distributed delays. Some new delay-dependent stochastic stability criteria are derived based on a novel Lyapunov–Krasovskii functional (LKF) approach. These new criteria based on the delay partitioning idea prove to be less conservative, since the conservatism could be notably reduced by thinning the delay partitioning. Numerical examples are provided to show the effectiveness and advantage of the proposed techniques.     

Stability analysis of Takagi-Sugeno stochastic fuzzy Hopfield neural networks with discrete and distributed time varying delays

In this paper, the global stability problem of Takagi-Sugeno (T-S) stochastic fuzzy Hopfield neural networks (TSSFHNNs) 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 TSSFHNNs with discrete and distributed time varying delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, in order to obtain stability region. In fact, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. The proposed stability conditions are demonstrated with numerical examples. Comparison with other stability conditions in the literature shows that our conditions are the more powerful ones to guarantee the widest stability region.     

时滞Hopfield神经网络的随机稳定性分析

T-S模型提供了一种通过模糊集和模糊推理将复杂的非线性系统表示为线性子模型的方法。研究了时滞Hopfield神经网络的随机稳定性（SFVDHNNs）。首先描述了SFVDHNNs模型,然后用Lyapunov方法研究了SFVDHNNs全局均方指数稳定性,通过可以被一些标准的数值分析方法求解的线性矩阵不等式（LMIs）得出了稳定性标准。     

Stability analysis for stochastic BAM neural networks with Markovian jumping parameters

This paper is concerned with the stability analysis issue for stochastic delayed bidirectional associative memory (BAM) neural network with Markovian jumping parameters. Assume that the jumping parameters are generated from continue-time discrete-state homogeneous Markov process and the delays are time-invariant. By employing the Lyapunov stability theory, some inequality techniques and the stochastic analysis, sufficient conditions are derived to achieve the global exponential stability in the mean square of the stochastic BAM neural network. One example is also provided in the end of this paper to illustrate the effectiveness of our results.     

Chaos and hyperchaos in a Hopfield neural network

In this paper we investigate numerically the parameter-space of an autonomous system of four nonlinear first-order ordinary differential equations, which represents a Hopfield neural network with four neurons. The study considers three independent two-dimensional cross-sections of the three-dimensional parameter-space generated by this mathematical model, every constructed considering Lyapunov exponent values. We show that is possible to completely characterize the dynamics of the system based in these three plots, which are representative of the three-dimensional parameter-space as a whole.     

受扰Hopfield神经网络L2增益稳定性分析

运用研究控制系统有限增益稳定的方法，讨论受扰Hopfield神经网络关于扰动的增益L2稳定，所给条件不但保证受扰网络L2增益稳定，且总能保证网络未受扰时唯一平衡点的存在性和全局渐近稳定性，文中结论还包含从扰动到状态的L2增益估计，它们用网络有关参数明确表达。     

一类具有时滞的广义Hopf ield 神经网络的全局稳定性

通过引入能量泛函，分析了一类具有时滞的广义Hopfield神经网络的全局稳定性．从理论上给出了该类网络为全局稳定的充分条件，证明了当时滞满足一个可计算的边界条件时，具有时滞的该类神经网络与相应的无时滞网络具有同样的全局稳定特性．仿真结果进一步证明了结论的有效性。     

不确定随机离散分布时滞神经网络的鲁棒稳定性*

采用Its微分公式和不等式分析技巧,研究了一类不确定随机离散分布时滞神经网络的鲁棒稳定性问题。该模型同时考虑了神经网络模型的两种扰动因素,即随机扰动与不确定性扰动。通过构造适当的Lyapunov泛函,以线性矩阵不等式形式给出了系统在均方根意义下的全局鲁棒稳定性判据,能够利用LMI工具箱很容易地进行检验。此外,仿真结果进一步证明了结论的有效性。     

Hopfield神经网络稳定性的敏感性研究

本文时一类非对称Hopfield神经网络在联接矩阵为非对称的前提下时矩阵特征值所在范围作了更精细的刻画：在有电阻(R)扰动下利用矩阵特征值理论给出了网络渐近稳定性的条件。     

Asymptotic stability of impulsive high-order Hopfield type neural networks

In this paper, we discuss impulsive high-order Hopfield type neural networks. Investigating their global asymptotic stability, by using Lyapunov function method, sufficient conditions that guarantee global asymptotic stability of networks are given. These criteria can be used to analyse the dynamics of biological neural systems or to design globally stable artificial neural networks. Two numerical examples are given to illustrate the effectiveness of the proposed method.     

时滞诱发的忆阻型Hopfield神经网络的复杂动力学

本文研究含时滞的忆阻型环状Hopfield神经网络的稳定性、Hopf分岔以及复杂振荡模式.根据特征方程根分布情况,获得了系统全时滞稳定条件和与时滞相关的稳定条件.通过数值计算揭示了丰富的动力学现象,如多种周期运动和混沌吸引子等,并给出了Poincaré截面上的分岔图.设计了电路实验平台,取得了与理论分析和数值计算高度吻合的实验结果.     

Hopfield网络的全局指数稳定性

在研究Hopfield神经网络时通常都假设输出响应函数是光滑的增函数.但实际应用中遇到的大多数函数都是非光滑函数.因此,本文将通常论文中Hopfield神经网络的输出响应函数连续可微的假设削弱为满足L ipschitz条件.通过引入Lyapunov函数的方法,证明了Hopfield神经网络全局指数收敛的一个充分性定理.并且由此定理获得该类网络全局指数稳定的几个判据.这定理与判据是近期相应文献主要结果的极大改进.     

脉冲Hopfield神经网络的鲁棒H-稳定性及其脉冲控制器设计

研究了脉冲Hopfield神经网络在Hopfield意义下的鲁棒稳定性. 通过应用Lyapunov函数法和Riccati不等式方法, 得到了脉冲Hopfield神经网络鲁棒稳定和鲁棒渐近稳定的充分条件, 在此基础上, 设计出了易于实施的脉冲控制器来镇定Hopfield神经网络. 最后, 给出了例子.     

Delay-dependent exponential state estimators for stochastic neural networks of neutral type with both discrete and distributed delays

This paper considered the state estimation for stochastic neural networks of neutral type with discrete and distributed delays. By using available output measurements, the state estimator can approximate the neuron states, and the asymptotic property of the state error is mean square exponential stable and also almost surely exponential stable in the presence of discrete and distributed delays. Under the Lipschitz assumptions for the activation functions and the measurement nonlinearity, a delay-dependent linear matrix inequality (LMI) criterion is proposed to guarantee the existence of the desired estimators by constructing an appropriate Lyapunov-Krasovskii function. It is shown that the existence conditions and the explicit expression of the state estimator can be parameterised in terms of the solution to a LMI. Finally, two numerical examples are presented to demonstrate the validity of the theoretical results and show that the theorem can provide less conservative conditions.     

Global exponential stability of impulsive high-order Hopfield type neural networks with delays

In this paper, we investigate the global exponential stability of impulsive high-order Hopfield type neural networks with delays. By establishing the impulsive delay differential inequalities and using the Lyapunov method, two sufficient conditions that guarantee global exponential stability of these networks are given, and the exponential convergence rate is also obtained. A numerical example is given to demonstrate the validity of the results.     

带有时滞的随机区间Hopfield神经网络的指数稳定性

讨论了带有可变时滞的随机区间Hopfield神经网络的指数稳定性, 利用It^o公式和Lyapunov函数, 得到了几个关于其指数稳定时滞无关和时滞相关的充分性条件, 推广了现有文献中关于定常时滞随机神经网络及其确定形式的许多结果.     

Novel delay-dependent global asymptotic stability condition of Hopfield neural networks with delays

In this paper, the global asymptotic stability of Hopfield neural networks with delays is investigated. Distinct differences from other analytical approaches lie in transforming to an equivalent system by using a parameterized transformation which allows free variables in an operator. A novel, less conservative and restrictive criterion than those established in the earlier references is given in terms of several matrix inequalities by utilizing the Lyapunov theory and matrix inequality framework. The results are related to the size of delays. Numerical examples are given to show the effectiveness of our proposed method.