共查询到20条相似文献,搜索用时 250 毫秒
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Meng Fan 《Journal of Mathematical Analysis and Applications》2005,309(2):598-625
This paper studies the dynamics of a system of retarded functional differential equations (i.e., RFDEs), which generalize the Hopfield neural network models, the bidirectional associative memory neural networks, the hybrid network models of the cellular neural network type, and some population growth model. Sufficient criteria are established for the globally exponential stability and the existence and uniqueness of pseudo almost periodic solution. The approaches are based on constructing suitable Lyapunov functionals and the well-known Banach contraction mapping principle. The paper ends with some applications of the main results to some neural network models and population growth models and numerical simulations. 相似文献
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The chaotic synchronization of Hindmarsh–Rose neural networks linked by a nonlinear coupling function is discussed. The HR neural networks with nearest-neighbor diffusive coupling form are treated as numerical examples. By the construction of a special nonlinear-coupled term, the chaotic system is coupled symmetrically. For three and four neurons network, a certain region of coupling strength corresponding to full synchronization is given, and the effect of network structure and noise position are analyzed. For five and more neurons network, the full synchronization is very difficult to realize. All the results have been proved by the calculation of the maximum conditional Lyapunov exponent. 相似文献
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研究球面神经网络的构造与逼近问题.利用球面广义的de la Vallee Poussin平均、球面求积公式及改进的单变量Cardaliaguet-Euvrard神经网络算子,构造具logistic激活函数的单隐层前向网络,并给出了Jackson型误差估计. 相似文献
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Projective Synchronization of Fractional Quaternion Neural Networks With Time-Varying Delays北大核心CSCD
研究了具有时变时滞的分数阶四元数神经网络的投影同步问题.该文不将分数阶四元数神经网络系统转化成两个复值系统或四个实值系统,而是将四元数系统当做一个整体进行处理.在合适的控制器下,通过构造合适的Lyapunov函数,并利用一些不等式技巧,得到了具有时变时滞分数阶四元数时滞神经网络投影同步的充分性判据.最后,通过数值仿真实例验证了所得结论的有效性和可行性. 相似文献
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近年来,前向神经网络泛逼近的一致性分析一直为众多学者所重视。本文系统分析三层前向网络对于拟差值保序函数族的一致逼近性,其中,转换函数σ是广义Sigmoidal函数。并将此一致性结果用于建立一类新的模糊神经网络(FNN),即折线FNN.研究这类网络对于两个给定的模糊函数的逼近性,相关结论在分析折线FNN的泛逼近性时起关键作用。 相似文献
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Different methodologies have been introduced in recent years with the aim of approximating unknown functions. Basically, these methodologies are general frameworks for representing non-linear mappings from several input variables to several output variables. Research into this problem occurs in applied mathematics (multivariate function approximation), statistics (nonparametric multiple regression) and computer science (neural networks). However, since these methodologies have been proposed in different fields, most of the previous papers treat them in isolation, ignoring contributions in the other areas. In this paper we consider five well known approaches for function approximation. Specifically we target polynomial approximation, general additive models (Gam), local regression (Loess), multivariate additive regression splines (Mars) and artificial neural networks (Ann).Neural networks can be viewed as models of real systems, built by tuning parameters known as weights. In training the net, the problem is to find the weights that optimize its performance (i.e. to minimize the error over the training set). Although the most popular method for Ann training is back propagation, other optimization methods based on metaheuristics have recently been adapted to this problem, outperforming classical approaches. In this paper we propose a short term memory tabu search method, coupled with path relinking and BFGS (a gradient-based local NLP solver) to provide high quality solutions to this problem. The experimentation with 15 functions previously reported shows that a feed-forward neural network with one hidden layer, trained with our procedure, can compete with the best-known approximating methods. The experimental results also show the effectiveness of a new mechanism to avoid overfitting in neural network training. 相似文献
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This note examines issues concerning global exponential convergence of neural networks with unbounded distributed delays. Sufficient conditions are derived by exploiting exponentially fading memory property of delay kernel functions. The method is based on comparison principle of delay differential equations and does not need the construction of any Lyapunov functionals. It is simple yet effective in deriving less conservative exponential convergence conditions and more detailed componentwise decay estimates. The results of this note and [Chu T. An exponential convergence estimate for analog neural networks with delay. Phys Lett A 2001;283:113–8] suggest a class of neural networks whose globally exponentially convergent dynamics is completely insensitive to a wide range of time delays from arbitrary bounded discrete type to certain unbounded distributed type. This is of practical interest in designing fast and reliable neural circuits. Finally, an open question is raised on the nature of delay kernels for attaining exponential convergence in an unbounded distributed delayed neural network. 相似文献
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Indicator space configuration for early warning of violent political conflicts by genetic algorithms
Recognition of preconflict situations has a powerful potential for early warning of violent political conflicts. This paper
focuses on the design and application of artificial neural networks as classifiers of preconflict situations. Achieving a
desired level of performance of the neural network relies on the appropriate construction of recognition space (selection
of indicators) and the choice of network architecture. A fast and effective method for the design of reliable neural recognition
systems is described. It is based on genetic algorithm techniques and optimizes both the configuration of input space and
the network parameters. The implementation of the methodology provides for increased performance of the classifier in terms
of accuracy, generalization capacity, computational and data requirements.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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B Baesens T Van Gestel M Stepanova D Van den Poel J Vanthienen 《The Journal of the Operational Research Society》2005,56(9):1089-1098
Traditionally, credit scoring aimed at distinguishing good payers from bad payers at the time of the application. The timing when customers default is also interesting to investigate since it can provide the bank with the ability to do profit scoring. Analysing when customers default is typically tackled using survival analysis. In this paper, we discuss and contrast statistical and neural network approaches for survival analysis. Compared to the proportional hazards model, neural networks may offer an interesting alternative because of their universal approximation property and the fact that no baseline hazard assumption is needed. Several neural network survival analysis models are discussed and evaluated according to their way of dealing with censored observations, time-varying inputs, the monotonicity of the generated survival curves and their scalability. In the experimental part, we contrast the performance of a neural network survival analysis model with that of the proportional hazards model for predicting both loan default and early repayment using data from a UK financial institution. 相似文献
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Amir Hosein Hadian Rasanan Nastaran Bajalan Kourosh Parand Jamal Amani Rad 《Mathematical Methods in the Applied Sciences》2020,43(3):1437-1466
By the rapid growth of available data, providing data-driven solutions for nonlinear (fractional) dynamical systems becomes more important than before. In this paper, a new fractional neural network model that uses fractional order of Jacobi functions as its activation functions for one of the hidden layers is proposed to approximate the solution of fractional differential equations and fractional partial differential equations arising from mathematical modeling of cognitive-decision-making processes and several other scientific subjects. This neural network uses roots of Jacobi polynomials as the training dataset, and the Levenberg-Marquardt algorithm is chosen as the optimizer. The linear and nonlinear fractional dynamics are considered as test examples showing the effectiveness and applicability of the proposed neural network. The numerical results are compared with the obtained results of some other networks and numerical approaches such as meshless methods. Numerical experiments are presented confirming that the proposed model is accurate, fast, and feasible. 相似文献
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连续型BAM神经网络的指数稳定性 总被引:1,自引:0,他引:1
首先将连续型双向联想记忆神经网络转化成一个特殊的Hopfield网络模型.在此基础上,对连续BAM神经网络的指数稳定性进行了新的分析,证明了神经网络连接权矩阵在给定的约束条件下有唯一平衡点.所做的分析可以用于设计全局指数稳定的神经网络. 相似文献
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《Nonlinear Analysis: Real World Applications》2008,9(5):1894-1904
In this paper, the global asymptotic stability of Hopfield neural networks (HNNs) with delays is investigated by utilizing Lyapunov functional method and the linear matrix inequality (LMI) technique. Distinct difference from other analytical approaches lies in “linearization” of the neural network model, by which the considered neural network model is transformed into a linear time-variant system. Then, a process, which is called parameterized first-order model transformation, is used to transform the linear system. Novel criteria for global asymptotic stability of the unique equilibrium point of delayed HNNs are obtained. The results are related to the size of delays. The obtained results are less conservative and restrictive than those established in the earlier references. Two numerical examples are given to show the effectiveness of our proposed method. 相似文献
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In this paper, we consider using the neural networks to efficiently solve the second-order cone constrained variational inequality
(SOCCVI) problem. More specifically, two kinds of neural networks are proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions
of the SOCCVI problem. The first neural network uses the Fischer-Burmeister (FB) function to achieve an unconstrained minimization
which is a merit function of the Karush-Kuhn-Tucker equation. We show that the merit function is a Lyapunov function and this
neural network is asymptotically stable. The second neural network is introduced for solving a projection formulation whose
solutions coincide with the KKT triples of SOCCVI problem. Its Lyapunov stability and global convergence are proved under
some conditions. Simulations are provided to show effectiveness of the proposed neural networks. 相似文献
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The paper introduces a new approach to analyze the stability of neural network models without using any Lyapunov function. With the new approach, we investigate the stability properties of the general gradient-based neural network model for optimization problems. Our discussion includes both isolated equilibrium points and connected equilibrium sets which could be unbounded. For a general optimization problem, if the objective function is bounded below and its gradient is Lipschitz continuous, we prove that (a) any trajectory of the gradient-based neural network converges to an equilibrium point, and (b) the Lyapunov stability is equivalent to the asymptotical stability in the gradient-based neural networks. For a convex optimization problem, under the same assumptions, we show that any trajectory of gradient-based neural networks will converge to an asymptotically stable equilibrium point of the neural networks. For a general nonlinear objective function, we propose a refined gradient-based neural network, whose trajectory with any arbitrary initial point will converge to an equilibrium point, which satisfies the second order necessary optimality conditions for optimization problems. Promising simulation results of a refined gradient-based neural network on some problems are also reported. 相似文献
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This paper investigates the use of neural network combining methods to improve time series forecasting performance of the traditional single keep-the-best (KTB) model. The ensemble methods are applied to the difficult problem of exchange rate forecasting. Two general approaches to combining neural networks are proposed and examined in predicting the exchange rate between the British pound and US dollar. Specifically, we propose to use systematic and serial partitioning methods to build neural network ensembles for time series forecasting. It is found that the basic ensemble approach created with non-varying network architectures trained using different initial random weights is not effective in improving the accuracy of prediction while ensemble models consisting of different neural network structures can consistently outperform predictions of the single ‘best’ network. Results also show that neural ensembles based on different partitions of the data are more effective than those developed with the full training data in out-of-sample forecasting. Moreover, reducing correlation among forecasts made by the ensemble members by utilizing data partitioning techniques is the key to success for the neural ensemble models. Although our ensemble methods show considerable advantages over the traditional KTB approach, they do not have significant improvement compared to the widely used random walk model in exchange rate forecasting. 相似文献
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《Applied Numerical Mathematics》2006,56(3-4):423-432
We compare piecewise linear and polynomial collocation approaches for the numerical solution of a Fredholm integro-differential equations modelling neural networks. Both approaches combine the use of Gaussian quadrature rules on an infinite interval of integration with interpolation to a uniformly distributed grid on a bounded interval. These methods are illustrated by numerical experiments on neural networks equations. 相似文献
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Prediction of tides is very much essential for human activities and to reduce the construction cost in marine environment. This paper presents two methods (1) an application of the functional networks (FN) and (2) sequential learning neural network (SLNN) procedures for the accurate prediction of tides using very short-term observation. This functional network model predicts the time series data of hourly tides directly while using an efficient learning process by minimizing the error based on the observed data for 30 days. Using the functional network, a very simple equation in the form of finite difference equation using the tidal levels at two previous time steps is arrived at. Sequential learning neural network uses one hidden neuron to predict the current tidal level using the previous four levels quite accurately. Hourly tidal data measured at Taichung harbor and Mirtuor coast along the Taiwan coastal region have been used for testing the functional network and sequential neural network model. Results show that the hourly data on tides for even a month can be predicted efficiently with a very high correlation coefficient. 相似文献
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V. I. Gorbachenko M. V. Zhukov 《Computational Mathematics and Mathematical Physics》2017,57(1):145-155
A neural network method for solving boundary value problems of mathematical physics is developed. In particular, based on the trust region method, a method for learning radial basis function networks is proposed that significantly reduces the time needed for tuning their parameters. A method for solving coefficient inverse problems that does not require the construction and solution of adjoint problems is proposed. 相似文献