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Abstract: The discrete delayed Hopfield neural networks is an extension of the discrete Hopfield neural networks. In this paper, the convergence of discrete delayed Hopfield neural networks is mainly studied, and some results on the convergence are obtained by using Lyapunov function. Several new sufficient conditions for the delayed networks converging towards a limit cycle with period at most 2 are proved in parallel updating mode. Also, some conditions for the delayed networks converging towards a limit cycle with 2-period are investigated in parallel updating mode. All results established in this paper extend the previous results on the convergence of both the discrete Hopfield neural networks, and the discrete delayed Hopfield neural networks in parallel updating mode. [Copyright &y& Elsevier]

Efficient computation of eigenvectors and eigenvalues of a matrix is an important problem in engineering, especially for computing eigenvectors corresponding to largest or smallest eigenvalues of a matrix. This paper proposes a neural network based approach to compute eigenvectors corresponding to the largest or smallest eigenvalues of any real symmetric matrix. The proposed network model is described by differential equations, which is a class of continuous time recurrent neural network model. It has parallel processing ability in an asynchronous manner and can achieve high computing performance. This paper provides a clear mathematical understanding of the network dynamic behaviors relating to the computation of eigenvectors and eigenvalues. Computer simulation results show the computational capability of the network model. [Copyright &y& Elsevier]

Abstract: Employing the matrix measure approach and Lyapunov function, the author studies the global exponential stability of delayed neural networks with impulses in this paper. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point for such delayed neural networks with impulses. Finally, three examples are given to show the effectiveness of the results obtained here. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: The stability of a class of stochastic Recurrent Neural Networks with time-varying delays is investigated in this paper. With the help of the Lyapunov function and the Dini derivative of the expectation of “along” the solution of the model, a set of novel sufficient conditions on mean square exponential stability has been established. An example is also given to illustrate the effectiveness of our results. [Copyright &y& Elsevier]

Abstract: In this paper high-order Hopfield neural networks (HHNNs) with time-varying delays are considered. Sufficient conditions for the existence and exponential stability of anti-periodic solutions are established, which are new and complement previously known results. [Copyright &y& Elsevier]

Abstract: This paper investigates the robust control problem for a class of neural networks subject to bounded uncertainties and time-varying delays. A memoryless decentralized variable structure control law with dead-zone input for guaranteeing global asymptotical system stability is derived. The results demonstrate that the derived control law does not restrict the derivative of the time-varying delays even if dead-zone nonlinearity occurs in the control input. Such a control law can be used to stabilize Cohen–Grossberg neural networks, cellular neural networks and Hopfield neural networks; all of which have bounded uncertainties and time-varying delays. Two examples are provided to illustrate the effectiveness and validity of the proposed control scheme. [Copyright &y& Elsevier]

Abstract: Minor component analysis (MCA) is an important statistical tool for signal processing and data analysis. Neural networks can be used to extract online minor component from input data. Compared with traditional algebraic approaches, a neural network method has a lower computational complexity. Stability of neural networks learning algorithms is crucial to practical applications. In this paper, we propose a stable MCA neural networks learning algorithm, which has a more satisfactory numerical stability than some existing MCA algorithms. Dynamical behaviors of the proposed algorithm are analyzed via deterministic discrete time (DDT) method and the conditions are obtained to guarantee convergence. Simulations are carried out to illustrate the theoretical results achieved. [Copyright &y& Elsevier]

Abstract: In this paper, we study simple algorithms for tracking objects in a video sequence, based on the selection of landmark points representative of the moving objects in the first frame of the sequence to be analyzed. The movement of these points is estimated using a sparse optical-flow method. Methods of this kind are fast, but they are not very robust. Particularly, they are not able to handle the occlusion of the moving objects in the video. To improve the performance of optical flow-based methods, we propose the use of adaptive filters and neural networks to predict the expected instantaneous velocities of the objects, using the predicted velocities as indicators of the performance of the tracking algorithm. The efficiency of these strategies in handling occlusion problems are tested with a set of synthetic and real video sequences. [Copyright &y& Elsevier]

This paper is concerned with existence and global exponential stability of periodic solutions for a class of Cohen–Grossberg neural networks with bounded and unbounded delays. By the continuation theorem of coincidence degree theory and differential inequality techniques, we deduce some sufficient conditions ensuring existence as well as global exponential stability of periodic solution. These conditions in our results are milder and less restrictive than that of previous known criteria since the hypothesis of boundedness and differentiability on the activation function are dropped. The theoretical analysis are verified by numerical simulations. [Copyright &y& Elsevier]

As the efficient calculation of eigenpairs of a matrix, especially, a general real matrix, is significant in engineering, and neural networks run asynchronously and can achieve high performance in calculation, this paper introduces a recurrent neural network (RNN) to extract some eigenpair. The RNN, whose connection weights are dependent upon the matrix, can be transformed into a complex differential system whose variable is a complex vector. By the analytic expression of , the convergence properties of the RNN are analyzed in detail. With general nonzero initial complex vector, the RNN obtains the largest imaginary part of all eigenvalues. By a rearrangement of connection matrix, the largest real part is obtained. A practice of a 7×7 matrix indicates the validity of this method. Two matrices, whose dimensionalities are 50 and 100, respectively, are employed to test the efficiency of this approach when dimension number becomes large. The results imply that the iteration number at which the network enters into equilibrium state is not sensitive with dimensionality. This RNN can be used to estimate the largest modulus of eigenvalues, etc. Compared with other neural networks designed for the similar aims, this RNN is applicable to general real matrices. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of asymptotic synchronization for a class of neural networks with reaction-diffusion terms and time-varying delays is investigated. Using the drive-response concept, a control law is derived to achieve the state synchronization of two identical neural networks with reaction-diffusion terms. Moreover, we derive a sufficient asymptotic synchronization condition for the neural networks with reaction-diffusion terms if reaction-diffusion terms satisfy a weaker condition. The synchronization condition is easy to verify and relies on the connection matrix in the driven networks and the suitable designed controller gain matrix in the response networks. [Copyright &y& Elsevier]

Abstract: In this paper, the conditions ensuring existence, uniqueness, and global exponential stability of the equilibrium point of a class of neural networks with variable delays are studied. Without assuming global Lipschitz conditions on these activation functions, applying idea of vector Lyapunov function, the sufficient conditions for global exponential stability of neural networks are obtained. [Copyright &y& Elsevier]

Abstract: Neural networks are widely used in many applications including astronomical physics,image processing, recognition, robotics, and automated target tracking, etc. Their ability to approximate arbitrary functions is the main reason for this popularity. In this paper, we discuss the constructive approximation on the whole real line by a neural networks with a sigmoidal activation function and a fixed weight. Using the convolution method, we show neural network approximation with a fixed weight to a continuous function on a compact interval. Also, we demonstrate a computational work that shows good agreement with theory. [Copyright &y& Elsevier]

Mathematical essence and structures of the feedforward neural networks are investigated in this paper. The interpolation mechanisms of the feedforward neural networks are explored. For example, the well-known result, namely, that a neural network is an universal approximator, can be concluded naturally from the interpolative representations. Finally, the learning algorithms of the feedforward neural networks are discussed. [Copyright &y& Elsevier]

This paper develops a general purpose numerical method to compute the feedback Nash equilibria in dynamic games. Players'' feedback strategies are first approximated by neural networks which are then trained online by parallel genetic algorithms to search over all time-invariant equilibrium strategies synchronously. To eliminate the dependence of training on the initial conditions of the game, the players use the same stationary feedback policies (the same networks), to repeatedly play the game from a number of initial states at any generation. The fitness of a given feedback strategy is then computed as the sum of payoffs over all initial states. The evolutionary equilibrium of the game between the genetic algorithms is the feedback Nash equilibrium of the dynamic game. An oligopoly model with investment is approximated as a numerical example. [Copyright &y& Elsevier]