Stability of discrete Hopfield neural networks with delay

Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. As it is well known, the stability of neural networks is not only the most basic and important problem but also foundation of the network＇s applications. The stability of discrete HJopfield neural networks with delay is mainly investigated by using Lyapunov function. The sufficient conditions for the networks with delay converging towards a limit cycle of length 4 are obtained. Also, some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle with length 2. The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.

Synchronization criteria for coupled Hopfield neural networks with time-varying delays

This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov Krasovskii＇s functional and use of Finsler＇s lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities （LMIs） which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

More relaxed condition for dynamics of discrete time delayed Hopfield neural networks

The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.

A Note on ＂Global Exponential Convergence Analysis of Hopfield Neural Networks with Continuously Distributed Delays＂

In this note, we would like to point out that （i） of Corollary 1 given by Zhang et al. （cf Commun. Theor. Phys. 39 （2003） 381） is incorrect in general.

Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.

New Delay-dependent Global Asymptotic Stability Condition for Hopfield Neural Networks with Time-varying Delays

This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This criterion is expressed in terms of linear matrix inequalities （LMIs）, which can be easily checked by utilizing the recently developed algorithms for solving LMIs. Examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed condition.

New Results of Global Asymptotical Stability for Impulsive Hopfield Neural Networks with Leakage Time-Varying Delay

In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kravsovskii functional, model transformation and some analysis techniques. The criterion of stability depends on the impulse and the bounds of the leakage time-varying delay and its derivative, and is presented in terms of a linear matrix inequality (LMI).

Delay-dependent Criteria for Robust Stability of Uncertain Switched Hopfield Neural Networks

This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functionals are constructed and the linear matrix inequality （LMI） approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence, uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties. By using Leibniz-Newton formula, free weighting matrices are employed to express this relationship, which implies that the new criteria are less conservative than existing ones. Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.

Robust stability for stochastic interval delayed Hopfield neural networks

A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.

Novel criteria for global exponential stability and periodic solutions of delayed Hopfield neural networks

The global exponentially stability and the existence of periodic solutions of a class of Hopfield neural networks with time delays are investigated. By constructing a novel Lyapunov function, new criteria are provided to guarantee the global exponentially stability of such systems. For the delayed Hopfield neural networks with time-varying external inputs, new criteria are also acquired for the existence and exponentially stability of periodic solutions. The results are generalizations and improvements of some recent achievements reported in the literature on networks with time delays.

改进离散Hopfield神经网络在煤矿人因评估中的应用

为了预防和控制煤矿人因事故发生,将离散Hopfield神经网络应用于煤矿人因安全评估中。首先根据人因分析与分类系统(Human Factors Analysis and Classification System,HFACS)模型建立煤矿人因安全风险评估体系,体系包含多个指标;其次是构建输入矩阵,借助模糊综合评价法对评估指标量化编码;最后,运用学习率优化的离散Hopfield神经网络展开煤矿人因安全评估,以模型输出结果确定评估对象风险等级。将构建的煤矿人因安全评估模型与传统评估方法进行比较,结果表明该模型合理有效,可用于煤矿人因安全评估,为煤矿人因安全管理提供依据。

GLOBAL EXPONENTIAL STABILITY IN HOPFIELD AND BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH TIME DELAYS

Without assuming the boundedness, strict monotonicity and differentiability of the activation functions, the authors utilize the Lyapunov functional method to analyze the global convergence of some delayed models. For the Hopfield neural network with time delays, a new sufficient condition ensuring the existence, uniqueness and global exponential stability of the equilibrium point is derived. This criterion concerning the signs of entries in the connection matrix imposes constraints on the feedback matrix independently of the delay parameters. From a new viewpoint, the bidirectional associative memory neural network with time delays is investigated and a new global exponential stability result is given.

Bogdanov–Takens Bifurcation in a Neutral Delayed Hopfield Neural Network with Bidirectional Connection

In this paper,a neutral Hopfield neural network with bidirectional connection is considered.In the first step,by choosing the connection weights as parameters bifurcation,the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system.In the second step,we studied the zeros of a third degree exponential polynomial in order to make sure that except the double zero root,all the other roots of the characteristic equation have real parts that are negative.Moreover,we find the critical values to guarantee the existence of the Bogdanov–Takens bifurcation.In the third step,the normal form is obtained and its dynamical behaviors are studied after the use of the reduction on the center manifold and the theory of the normal form.Furthermore,for the demonstration of our results,we have given a numerical example.

Almost Automorphic Solutions for Quaternion-Valued Hopfield Neural Networks with Mixed Time-Varying Delays and Leakage Delays

This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks.The results are completely new.Finally,the authors give an example to illustrate the feasibility of the results.

离散Hopfield神经网络的稳定性研究

推广了前人关于离散Ｈｏｐｆｉｅｌｄ 神经网络的稳定性定理及周期为２ 极限环的存在定理，并从理论上给出了新的严格的证明．进一步，提出了关于部分变元稳定和部分变元为极限环的新概念，并给出了判别定理．最后给出了几个有趣的例子，揭示这类网络渐近行为的复杂性．

离散Hopfield神经网络的稳定性研究

离散Hopfield神经网络的稳定性是网络应用的基础 .文中主要研究非对称离散Hopfield神经网络的异步、同步、部分同步演化方式的稳定性 ,并给出了一些新的稳定性条件 ,所获结果推广了一些已有的结论 .

延迟离散Hopfield型神经网络异步收敛性

离散Ｈｏｐｆｉｅｌｄ型神经网络的一个重要性质是异步运行方式下总能收敛到稳定态；同步运行方式下总能收敛到周期不超过２的极限环．它是该模型可以用于联想记忆设计、组合优化计算的理论基础．文中给出了延迟离散Ｈｏｐｆｉｅｌｄ型网络的收敛性定理．在异步运行方式下，证明了对称连接权阵的收敛性定理，推广了已有的离散Ｈｏｐ－ｆｉｅｌｄ型网络的收敛性结果，给出了能量函数极大值点与延迟离散Ｈｏｐｆｉｅｌｄ型网络的稳定态的关系及稳定态邻域的演化特征，得到了能量函数收敛与异步运行时网络达到稳定的协调关系．

基于离散Hopfield网络求解极大独立集的茎区选择算法以及在RNA二级结构预测中的应用

提出了一种利用离散Hopfield网络求解图论极大独立集的启发式算法,并将其应用于RNA二级结构的茎区选择和预测当中.算法通过映射RNA序列的茎区为无向图中的节点,将预测RNA二级结构的问题转化为求解图的极大独立集的问题.定义了合理的能量变化函数,利用离散Hopfield网络进行迭代,以获得能量最优的预测结构.文中将算法与传统的最大匹配数算法以及最小自由能算法在运行时间上进行比较,并且选择特定的序列在茎区和碱基对水平上进行精度测试,结果证明该算法在效率和精度上具有一定的优势.算法的时间复杂性为max{O(n2),O(N2)},空间复杂度为O(N2),其中n为RNA序列长度,N为RNA的茎区段个数.

不同演化模式的离散Hopfield网络的稳定性研究

神经网络的稳定性被认为是神经网络应用的基础。研究了非对称离散Hopfield神经网络的异步、同步、部分同步演化方式的稳定性 ,证明得到对于已知稳定的网络 ,如果经其连接权矩阵一定的增量 ,得到一个新的连接权矩阵 ,则在一定条件下可保证所得新的网络仍是稳定的。所获结果不仅推广了已有的结论 ,而且为离散Hopfield神经网络稳定性的稳健性能分析和应用提供了理论基础。

基于离散Hopfield模式识别样本的GRNN非线性组合短期风速预测模型

利用实时风速数据,建立基于离散Hopfield模式识别样本的广义回归神经网络(GRNN)非线性组合预测模型。在风速数据样本集经二维小波阈值去噪处理后,基于离散Hopfield识别历史数据中与待预测样本最相似的数据,并作为训练样本;将支持向量机、BP神经网络和Elman神经网络分别进行单项预测的结果作为输入向量,经GRNN进行非线性组合预测。采用某风电场的实际风速数据进行预测,结果验证了该预测模型的正确性和有效性。