System identification based on NARMAX model using Hopfield networks

An approach is proposed to avoid model structure determination in system identification using NARMAX （nonlinear autoregressive moving average with exogenous inputs） model. Identification procedure is formulated as an optimization procedure of a apecial class of Hopfield network in the proposed approach. The particular structure of these Hopfield networks can avoid the local optimum problem. Training of these Hopfield network achieves model structure determination and parameter estimation. Convergence of Hopfield networks guarantees that a NARMAX model of random initial state will approach a valid identification model with accurate state parameters. Results of two simulation examples illustrate that this approach is efficient and simple.

A new chaotic Hopfield network with piecewise linear activation function

This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.

Hierarchical control based on Hopfield network for nonseparable opti mization problems

The nonseparable optimization control problem is considered, where the overall objective function is not of an additive form with respect to subsystems. Since there exists the problem that computation is very slow when using iteratire algorithms in multiobjective optimization, Hopfield optimization hierarchical network based on IPM is presented to overcome such slow computation difficulty. Asymptotic stability of this Hopfield network is proved and its equilibrium point is the optimal point of the original problem. The simulation shows that the net is effective to deal with the optimization control problem for large-scale non.separable steady state systems.

State Sampling Dependence of Hopfield Network Inference

The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations.We present the system in the glassy phase with low temperature and high memory load.We find that the inference error is very sensitive to the form of state sampling.When a single state is sampled to compute magnetizations and correlations,the inference error is almost indistinguishable irrespective of the sampled state.However,the error can be greatly reduced if the data is collected with state transitions.Our result holds for different disorder samples and accounts for the previously observed large fluctuations of inference error at low temperatures.

Exponential Stability of Periodic Solution for Delayed Hopfield Networks

纸与构造 Lyapunov functionals 并且使用不平等技术的 time-varying.By 被奉献给推迟的 Hopfield 神经网络的周期的引起注意的人，一些新足够的标准被获得保证存在和周期的 attractor.Our 结果的全球指数的稳定性改进并且延长一些存在的在[ 1314 ] .One 例子也被得出表明我们的结果的优点。

Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption

The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits.This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network(HNN)with coupled hyperbolic memristors through the modification of a single coupling connection weight.The bistable mode of the hyperbolic memristive HNN(mHNN),characterized by the coexistence of asymmetric chaos and periodic attractors,is effectively demonstrated through the utilization of conventional nonlinear analysis techniques.These techniques include bifurcation diagrams,two-parameter maximum Lyapunov exponent plots,local attractor basins,and phase trajectory diagrams.Moreover,an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors.This method demonstrates significant benefits in correlation,information entropy,and resistance to differential attacks,providing strong evidence for its effectiveness in encryption.Additionally,an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN.The correctness of the circuit design is confirmed through Multisim simulations,which align with numerical simulations conducted in Matlab.

离散Hopfield神经网络在职业院校学生综合素养评价中的应用研究

为克服教育评估中人为因素的干扰,提高评估的准确性和效率,该文探索将离散Hopfield神经网络应用到职业院校学生综合素养的评价中。Matlab仿真发现,通过设置合适的神经元平衡点,离散Hopfield神经网络可根据输入的指标数据对学生的职业综合素养给出有效的评估,评估结果与专家评估的结果完全一致。

随机时滞Hopfield神经网络分步θ方法的一般衰减率稳定性

旨在研究随机时滞Hopfield神经网络分步θ方法的一般衰减率稳定性。当θ∈[0,1/2)时,在步长受限的条件下,随机时滞Hopfield神经网络分步θ方法是一般衰减率稳定的。对于θ∈[1/2,1],不需要额外的步长要求,即可保证随机时滞Hopfield神经网络分步θ方法的一般衰减率稳定性。最后,通过一个数值例子验证所得结果的有效性。

概反周期函数及其在一类Hopfield神经网络上的应用

探讨一类具有混合时滞的中立型Hopfield神经网络的概反周期解的存在性与稳定性。首先,讨论了概周期函数与概反周期函数之间的关系,证明了全体概反周期函数构成的集合,是概周期函数空间的一个闭子空间。最后,利用不动点原理得到Hopfield神经网络存在一个唯一的有界解,而且该解函数还是概反周期函数。概反周期函数是比概周期函数更精细的函数,对神经网络概反周期解的存在性与唯一性的探讨,相较于对概周期解的存在性以及唯一性的探讨,能够更加精确地描述神经网络的动力学性质,所得结论是新颖的,是现有结论的进一步完善与补充。

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。

Hopfield neural network based on ant system

Hopfield neural network is a single layer feedforward neural network. Hopfield network requires some control parameters to be carefully selected, else the network is apt to converge to local minimum. An ant system is a nature inspired meta heuristic algorithm. It has been applied to several combinatorial optimization problems such as Traveling Salesman Problem, Scheduling Problems, etc. This paper will show an ant system may be used in tuning the network control parameters by a group of cooperated ants. The major advantage of this network is to adjust the network parameters automatically, avoiding a blind search for the set of control parameters. This network was tested on two TSP problems, 5 cities and 10 cities. The results have shown an obvious improvement.

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.

Convergence in Continuous Hopfield Neural Network with Delays

A sufficient condition are derived for the global asymptotic stability of the equilibrium of continuous Hopfield neural networks with delays of the

A novel chaotic system with one source and two saddle-foci in Hopfield neural networks

This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional （3D） autonomous continuous time Hopfield neural network. In particular, the system with one source and two saddle-foci has a chaotic attractor and a periodic attractor with different initial points, which has rarely been reported in 3D autonomous systems. The complex dynamical behaviours of the system are further investigated by means of a Lyapunov exponent spectrum, phase portraits and bifurcation analysis. By virtue of a result of horseshoe theory in dynamical systems, this paper presents rigorous computer-assisted verifications for the existence of a horseshoe in the system for a certain parameter.

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.

ON THE ASYMPTOTIC BEHAVIOR OF HOPFIELD NEURAL NETWORK WITH PERIODIC INPUTS

Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.

Existence and Exponential Stability of Almost Periodic Solution for Hopfield Neural Network Equations with Almost Periodic Imput

By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.

A New Sequential Detection Based on Hopfield Neural Network in Frequency Selective Fading Channels

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负阻态忆阻Hopfield神经网络动力学

人类大脑是一个高度复杂且规模庞大的非线性动力学系统,其动力学行为与人类智能活动密切相关。基于忆阻器的人工神经网络不仅可以很好地模拟人脑工作机制,而且其非线性特性可以为神经网络带来更为丰富的动力学行为。为了进一步发挥神经网络的优势,引入一种新的具有负阻态功能的忆阻器模型,该模型打破了原有忆阻器的阻态极性限制,为忆阻器扮演神经网络突触仿生器件提供了更加丰富的变化性能。在对忆阻器模型分析的基础上,提出了一种新的忆阻Hopfield神经网络(HNN),进一步加强了HNN的负反馈功能,使之表现出更加丰富和复杂的动力学行为。实验结果表明,新忆阻HNN拥有较为丰富的动力学行为,具有一定的混沌特性。在不同的忆阻器参数以及权值矩阵取值条件下,观察系统的相位轨迹图、Lyapunov指数的变化情况,并与同类型网络进行对比,进一步证明提出的神经网络的有效性,同时复杂的动力学特性也为在数据处理、图像加密等方面的应用提供了研究支撑。

Global asymptotic stability for Hopfield-type neural networks with diffusion effects

The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium （if it exists） is globally asymptotically stable and this implies that the equilibrium of the system is unique.