Delay-range-dependent exponential stability criteria and decay estimation for switched Hopfield neural networks of neutral type

This paper is concerned with the problem of delay-range-dependent global exponential stability and decay estimation for a class of switched Hopfield neural networks (SHNNs) of neutral type. An average dwell time method is introduced into switched Hopfield neural networks. By constructing a new Lyapunov–Krasovskii functional and designing a switching law, some criteria are proposed for guaranteeing exponential stability for a given system, while the exponential decay estimation is explicitly developed for the states. A numerical example is provided to demonstrate the effectiveness of the main results.     

具有跳跃的随机神经网络的均方稳定性

研究了一类新的具有脉冲跳跃的Hopfield神经网络系统模型,其中脉冲时刻的跳跃是由一般的随机序列所引起,通过运用Lyapunov函数方法,获取了一些新的均方稳定性结果.由于脉冲的跳跃使得不稳定的神经网络变成稳定,因而所得的结果也可以运用到其他相关领域.     

Stationary oscillation for high-order Hopfield neural networks with time delays and impulses

We investigate stationary oscillation for high-order Hopfield neural networks with time delays and impulses. In a recent paper [J. Zhang, Z. J. Gui, Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays, Journal of Computational and Applied Mathematics 224 (2008) 602-613], the authors claim that they obtain a criterion of existence, uniqueness, and global exponential stability of periodic solution (i.e. stationary oscillation) for high-order Hopfield neural networks with time delays and impulses. In this paper, we point out that the main result of the recent paper is unture, and present a new sufficient condition of stationary oscillation for the neural networks. A numerical example is given to illustrate the effectiveness of the obtained result.     

Exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays

This paper studies the problems of global exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential stability in the mean square for the reaction-diffusion high-order neural networks are established, which are easily verifiable and have a wider adaptive. An example is also discussed to illustrate our results.     

具有变时滞和脉冲效应的Hopfield神经网络的全局指数稳定性

讨论了一类具有变时滞和脉冲效应的Hopfield神经网络模型．利用按段连续的向量Liapunov思想方法,研究了脉冲时滞神经网络的全局指数稳定性．例子及其数值仿真说明了结果的有效性．推广和改进了已有文献的一些结果．     

Linear Matrix Inequality Optimization Approach to Exponential Robust Filtering for Switched Hopfield Neural Networks

This paper is concerned with the delay-dependent exponential robust filtering problem for switched Hopfield neural networks with time-delay. A new delay-dependent switched exponential robust filter is proposed that results in an exponentially stable filtering error system with a guaranteed robust performance. The design of the switched exponential robust filter for these types of neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated using standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed filter.     

带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性

讨论了带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性.通过构造合适的Lyapunov函数,获得了判定带马尔可夫跳的随机Hopfield神经网络的以分布渐近稳定性的充分条件.     

一类Hopfield神经网络系统的全局渐近稳定性

研究变系数具有连续分布时滞的Hopfield神经网络系统Ci(t)dxi/dt=-xi(t)/Ri(t) ∑j=1^nWij(t)fj[∫o^∞kj(s)xj(t-s)ds ] Ii(t)的全局渐近稳定性,获得了一个充分条件。     

时滞Hopfield神经网络模型的全局吸引性和全局指数稳定性

对具有时滞的Hopfield神经网络模型,在非线性神经元激励函数是Lipschitz连续(而非已有的大部分文献中假设是Sigmoid函数)的条件下,通过构造适当的泛函,给出了这类模型全局吸引和平衡点全局指数稳定的易于验证的充分条件。     

Stability analysis of fractional-order complex-valued neural networks with time delays

In this paper, we consider the problem of stability analysis of fractional-order complex-valued Hopfield neural networks with time delays, which have been extensively investigated. Moreover, the fractional-order complex-valued Hopfield neural networks with hub structure and time delays are studied, and two types of fractional-order complex-valued Hopfield neural networks with different ring structures and time delays are also discussed. Some sufficient conditions are derived by using stability theorem of linear fractional-order systems to ensure the stability of the considered systems with hub structure. In addition, some sufficient conditions for the stability of considered systems with different ring structures are also obtained. Finally, three numerical examples are given to illustrate the effectiveness of our theoretical results.     

Horseshoe chaos in a class of simple Hopfield neural networks

A class of new simple Hopfield neural networks is revisited. To confirm the chaotic behavior in these Hopfield neural networks demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a rigorous verification of existence of horseshoe chaos by virtue of topological horseshoes theory and estimates of topological entropy in the derived Poincaré maps.     

Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters

In this paper, the problem of stochastic stability for a class of time-delay Hopfield neural networks with Markovian jump parameters is investigated. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. Without assuming the boundedness, monotonicity and differentiability of the activation functions, some results for delay-dependent stochastic stability criteria for the Markovian jumping Hopfield neural networks (MJDHNNs) with time-delay are developed. We establish that the sufficient conditions can be essentially solved in terms of linear matrix inequalities.     

Hopfield neural networks in large-scale linear optimization problems

Hopfield neural networks and affine scaling interior point methods are combined in a hybrid approach for solving linear optimization problems. The Hopfield networks perform the early stages of the optimization procedures, providing enhanced feasible starting points for both primal and dual affine scaling interior point methods, thus facilitating the steps towards optimality. The hybrid approach is applied to a set of real world linear programming problems. The results show the potential of the integrated approach, indicating that the combination of neural networks and affine scaling interior point methods can be a good alternative to obtain solutions for large-scale optimization problems.     

STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH DELAYS

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Robust exponential stability analysis of discrete-time switched Hopfield neural networks with time delay

The robust exponential stability problem in this paper for discrete-time switched Hopfield neural networks with time delay and uncertainty is considered. Firstly, the mathematical model of the system is established. Then by constructing a new Lyapunov–Krasovskii functional, some new delay-dependent criteria are developed, which guarantee the robust exponential stability of discrete-time switched Hopfield neural networks. A numerical example is provided to demonstrate the potential and effectiveness of the results obtained.     

Hopfield神经网络的稳定性及其在投资组合中的应用

在取消了神经元之间的连接权系数对称限制的基础上 ,讨论了 Hopfield神经网络的稳定性 ,得到了一些有益结论 .并将其应用于 Hopfield神经网络算法的改进上 .进而依据改进的算法以有价证券的选择为例进行了随机模拟 ,取得了令人满意的结果 .     

The split-step θ-methods for stochastic delay Hopfield neural networks

In this paper, we construct a new split-step numerical method for stochastic delay Hopfield neural networks. The main aim of this paper is to investigate the mean-square stability of this split-step θ-methods for stochastic delay Hopfield neural networks. It is proved that the split-step θ-methods are mean-square stable under suitable conditions. Numerical experiments verify the numerical stability results obtained from theory. A comparison between this work and Ronghua et al. [8] is also discussed in the example.     

Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays

In this paper, by means of constructing the extended impulsive delayed Halanay inequality and by Lyapunov functional methods, we analyze the global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. Some new sufficient conditions ensuring exponential stability of the unique equilibrium point of impulsive Hopfield neural networks with time delays are obtained. Those conditions are more feasible than that given in the earlier references to some extent. Some numerical examples are also discussed in this work to illustrate the advantage of the results we obtained.     

New results for global stability of a class of neutral-type neural systems with time delays

This paper studies the global convergence properties of a class of neutral-type neural networks with discrete time delays. This class of neutral systems includes Cohen–Grossberg neural networks, Hopfield neural networks and cellular neural networks. Based on the Lyapunov stability theorems, some delay independent sufficient conditions for the global asymptotic stability of the equilibrium point for this class of neutral-type systems are derived. It is shown that the results presented in this paper for neutral-type delayed neural networks are the generalization of a recently reported stability result. A numerical example is also given to demonstrate the applicability of our proposed stability criteria.     

连续型BAM神经网络的指数稳定性

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.