区间时滞神经网络的随机稳定性

分析了区间变时滞的随机神经网络的全局渐进稳定性。区间变时滞不仅考虑了时变因素,而且考虑了时滞时变的上界和下界。通过Itô’s 微分公式和构造适当的李雅普罗夫泛函,并且引入自由权值矩阵,以线性矩阵不等式形式给出了该系统在均方意义下的全局渐进稳定的充分性判据。数值算例进一步证明了结论的有效性。     

时滞连续Hopfield神经网络的全局指数稳定性

本文采用非线性时滞微分不等式分析技巧,研究了时滞连续Hopfield神经网络的稳定性,给出在任意外界恒常输入下连续Hopfield网络的平衡态的收敛速度及全局指数稳定的若干充分判据.     

混杂型离散时间脉冲时滞Hopfield神经网络的多稳定性分析

研究一类混杂型离散时间脉冲时滞Hopfield神经网络的多稳定性问题。首先,运用Brouwer不动点定理,证明所考虑的脉冲时滞神经网络具有多个平衡点。然后,引入Lyapunov函数,运用不等式分析技术,建立脉冲离散时滞Hopfield神经网络多稳定性判别准则,并给出平衡点吸引域的估计。最后,通过数值实例仿真验证结果的有效性。     

时滞Hopfield神经网络的随机稳定性分析

T-S模型提供了一种通过模糊集和模糊推理将复杂的非线性系统表示为线性子模型的方法。研究了时滞Hopfield神经网络的随机稳定性（SFVDHNNs）。首先描述了SFVDHNNs模型,然后用Lyapunov方法研究了SFVDHNNs全局均方指数稳定性,通过可以被一些标准的数值分析方法求解的线性矩阵不等式（LMIs）得出了稳定性标准。     

具有区间时滞的不确定性随机时滞系统的时滞相关鲁棒稳定性

针对具有区间时滞的不确定性随机时滞系统, 进行稳定性分析. 通过考虑变时滞、时滞的上界及它们的差三者之间的关系, 并应用公式和Lyapunov稳定性理论, 在不忽略任何有用项的前提下, 得到改进的具有区间时滞的随机系统的稳定性判据. 数值实例验证了该方法的有效性.     

不确定时变时滞连续Hopfield神经网络的鲁棒稳定性

本文研究了时变时滞连续Hopfield神经网络存在有界参数不确定时的稳定性问题,提出了保证该网络鲁棒稳定的代数Riccati方程(ARE)设计算法.而忽略时滞或忽略参数不确定,则得到有别于以往结果的各种有关参数不确定连续Hopfield神经网络稳定性的定理.     

具有时滞的线性区间系统的鲁棒稳定性

本文给出了线性区间时滞系统鲁棒稳定性的一些结果，这些结果推广和是了前人关于线性时滞系统鲁棒稳定性的相关结论，同时还讨论了线性区间时滞系统的稳定度，最后讨论了线性区间时滞大系统的鲁棒稳定性。     

具分布参数的随机Hopfield神经网络的指数稳定

基于随机Fubini定理,将随机偏微分方程描述的Hopfield神经网络系统转化为用相应的随机常微分方程来描述.利用关于空间变量平均的Lyapunov函数与Ito^公式,通过对所构造的Lyapunov函数在Ito^微分规则下对相应系统求导的方法,获得了系统指数稳定的代数判据及其Lyapunov指数估计.实现了运用Lyapunov直接法对分布参数系统稳定性的研究.     

时滞脉冲型Hopfield神经网络的全局指数稳定性*

基于众多领域及生物神经网络本身所存在的脉冲瞬动现象，本文首次提出并研究了带时滞的脉冲型Ｈｏｐｆｉｅｌｄ神经网络的全局指定稳定性问题，并讨论了其平衡态的存在唯一性。     

不确定随机离散分布时滞神经网络的鲁棒稳定性*

采用Its微分公式和不等式分析技巧,研究了一类不确定随机离散分布时滞神经网络的鲁棒稳定性问题。该模型同时考虑了神经网络模型的两种扰动因素,即随机扰动与不确定性扰动。通过构造适当的Lyapunov泛函,以线性矩阵不等式形式给出了系统在均方根意义下的全局鲁棒稳定性判据,能够利用LMI工具箱很容易地进行检验。此外,仿真结果进一步证明了结论的有效性。     

Almost sure exponential stability of neutral stochastic delayed cellular neural networks

In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.     

Almost sure exponential stability of neutral stochastic delayed cellular neural networks

In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.     

On asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks

In this paper, we obtain some sufficient conditions for determining the asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks by utilizing the Lyapunov functional method. An example is given to show the validity of the results.     

Asymptotic stability of impulsive high-order Hopfield type neural networks

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.     

Exponential stability of stochastic delay interval systems

Although deterministic interval systems have received a great deal of attention, so far there is no work on stochastic interval systems. The main aim of this paper is to initiate the study of stochastic interval systems. Of course, there are many properties of such systems to be investigated, but this paper will concentrate on the study of exponential stability of stochastic interval systems with time-varying delays. The main technique used in this paper is the Razumikhin-type theorem established recently by Mao (Stochastic Process. Appl. 65 (1996) 233–250).     

Global exponential stability of impulsive high-order Hopfield type neural networks with delays

In this paper, we investigate the global exponential stability of impulsive high-order Hopfield type neural networks with delays. By establishing the impulsive delay differential inequalities and using the Lyapunov method, two sufficient conditions that guarantee global exponential stability of these networks are given, and the exponential convergence rate is also obtained. A numerical example is given to demonstrate the validity of the results.     

时延细胞神经网络的全局渐近稳定性

通过构造新的Lyapunov泛函,在Lyapunov泛函中巧妙引入可调的实参数,并结合不等式运用的一些技巧,讨论了时延细胞神经网络的全局渐近稳定性问题,得到了该模型的平衡点全局渐近稳定的一些新的充分条件。所得的结果改进推广了已有文献中相应的一些结论,并且可应用于以前所不能处理的若干情形。理论分析和数学推导表明,全局渐近稳定性的一个简单充分判据与时延是有关的。所得结果突出了时延对于细胞神经网络的全局渐近稳定性的影响,这对于设计带时延的细胞神经网络有着重要的参考价值。此外,通过实例说明了相应结果的应用,这在理论上和应用中都有着重要的意义。     

Novel delay-dependent stability condition for mixed delayed stochastic neural networks with leakage delay signals

In this paper, the problem of stability condition for mixed delayed stochastic neural networks with neutral delay and leakage delay is investigated. A novel Lyapunov functional is constructed with double and triple integral terms. New sufficient conditions are derived to guarantee the global asymptotic stability of the concerned neural network. This paper is more general than the paper by Zhu et al. [Robust stability of Markovian jump stochastic neural networks with time delays in the leakage terms, Neural Process. Lett. 41 (2015), pp. 1–27]. In our paper, we considered both the neutral delay and leakage delay, but the paper by Zhu et al. is not considering the neutral delay. Also we employed triple integrals in the Lyapunov functional which is not used in the paper by Zhu et al. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.