具有leakage时滞与随机干扰的离散神经网络渐近稳定性分析

研究了一类具有leakage时滞与随机干扰的离散型神经网络的全局渐近稳定性问题．利用一种新的时滞分割方法将时滞区间分割为多个区间．通过构造新的Lyapunov泛函得到了基于线性矩阵不等式（LMI）的渐近稳定性判据．该判据在获得更小的保守性同时也降低了计算的复杂度．     

潜伏期具有传染性的SEIRS流行病模型的全局稳定性

研究一类潜伏期和染病期均具有传染性和康复可能的SEIRS流行病模型,确定了疾病流行与否的阈值,利用Routh-Hurwitz判据和LaSalle不变集原理得到无病平衡点的全局渐近稳定性,并借助广义Bendixson-Dulac定理得到地方病平衡点的全局渐近稳定性,最后给出数值模拟.     

一类带有阈的神经网络模型的全局稳定性

利用分析技巧,获得了一类带有阈的神经网络模型全局稳定性的判据,去掉了文「１」相应结果的一个较强条件∫＾∞０ｓｋ（ｓ）ｄｓ〈＋∞。     

一类混合时滞的非线性耦合神经网络的同步

主要讨论了一类混合时滞的非线性耦合神经网络的同步问题.同时,考虑随机扰动以及参数的切换由某个马尔可夫链所确定等方面对其的影响.文中通过构造新的Lyapunov-Krasovskii泛函,运用线性矩阵不等式（LMI）技术并结合Kronecker积来获得神经网络全局同步的充分性判据.由于这样得到的判据是LMI形式,因此可以由数学软件Matlab的LMI Toolbox对所获得的判据进行有效的验证和求解.此外,本文中我们对细胞激活函数做了更为一般的假设,从而使结论在LMI下可以减少保守性.     

具有非单调传染率的SIQR传染病模型的稳定性分析

该文研究了一类具有非单调传染率的SIQR传染病模型,讨论了平衡点的存在性,运用特征值法、Hurwit判据和极限方程理论证明了当阈值R_01时无病平衡点是全局渐近稳定的;当R_01时,无病平衡点是不稳定的.并采用Lipunov函数法和Lasalle不变性原理证明了地方性平衡点是全局渐近稳定的.最后进行了数值模拟,验证了理论结果的有效性.     

具有时滞的细胞神经网络模型的全局指数稳定性

利用拓扑度理论、推广的Halanaly矩阵时滞微分不等式、Lyapunov原理以及Dini导数,研究了具有时滞的细胞神经网络模型的全局指数稳定性．去掉了有关文献中要求输出函数fj在实数集R上有界、可微的条件,给出了更弱的判定平衡点的存在唯一性以及全局指数稳定性的判据,推广和改进了前人的相关结论,最后的数值例子说明本文结果不仅保守性小,而且计算简单．     

一类谣言传播模型的全局稳定性

本文提出了一类具有媒体效应和标准传播率的谣言传播模型.基于谣言的基本再生数,分析了边界平衡点和正平衡点的存在性.利用Lyapunov-LaSalle不变集原理证明了边界平衡点的全局渐近稳定性,根据Routh-Hurwitz判据和广义Bendixson-Dulac定理证明了正平衡点的全局渐近稳定性.结果表明,媒体效应虽无法消除谣言,但能减小谣言传播的最终规模.数值例子验证了结论的有效性.     

变时延神经网络的全局指数稳定性及收敛性

利用Lyapunov泛函方法和线性矩阵不等式（LMI）技术,通过引入一系列参数,给出全局指数稳定的平衡点的判别条件和时延的最大上界和神经网络的收敛速度,所得结果较之一些文献中的结果简单、实用并且对于具体设计带时延神经网络有重要的指导意义.最后,通过实例表明给出的判定条件是有效、可行的.     

面向异步多时延基因调控网络建模的高阶动态贝叶斯网络模型及其结构 学习算法

目的：由基因芯片数据精确学习建模具有异步多时延表达调控关系的基因调控网络。方法：提出了一种高阶动态贝叶斯网 络模型,并给出了网络结构学习算法,该模型假定基因的调控过程为多阶马尔科夫过程,从而能够建模基因调控网络中的异步多 时延特性。结果：由酵母基因调控网络一个子网络人工生成了加入10%含噪声的表达数据用于调控网络结构学习。在75%的后验 概率下,本文提出的高阶动态贝叶斯网络模型能够正确建模实际网络中全部的异步多时延调控关系,而经典动态贝叶斯网络仅 能够正确建模实际网络中1/3的调控关系;ROC曲线对比表明在各个后验概率水平上高阶动态贝叶斯网络模型的效果均优于经 典动态贝叶斯网络。结论：本文提出的高阶动态贝叶斯网络模型能够精确学习建模具有异步多时延表达调控关系的基因调控网 络。     

面向异步多时延基因调控网络建模的高阶动态贝叶斯网络模型及其结构学习算法

目的：由基因芯片数据精确学习建模具有异步多时延表达调控关系的基因调控网络。方法：提出了一种高阶动态贝叶斯网络模型,并给出了网络结构学习算法,该模型假定基因的调控过程为多阶马尔科夫过程,从而能够建模基因调控网络中的异步多时延特性。结果：由酵母基因调控网络一个子网络人工生成了加入10%含噪声的表达数据用于调控网络结构学习。在75%的后验概率下,本文提出的高阶动态贝叶斯网络模型能够正确建模实际网络中全部的异步多时延调控关系,而经典动态贝叶斯网络仅能够正确建模实际网络中1/3的调控关系;ROC曲线对比表明在各个后验概率水平上高阶动态贝叶斯网络模型的效果均优于经典动态贝叶斯网络。结论：本文提出的高阶动态贝叶斯网络模型能够精确学习建模具有异步多时延表达调控关系的基因调控网络。     

Global and robust stability of interval Hopfield neural networks with time-varying delays

In this paper, we investigate the problem of global and robust stability of a class of interval Hopfield neural networks that have time-varying delays. Some criteria for the global and robust stability of such networks are derived, by means of constructing suitable Lyapunov functionals for the networks. As a by-product, for the conventional Hopfield neural networks with time-varying delays, we also obtain some new criteria for their global and asymptotic stability.     

Mean square stability of uncertain stochastic BAM neural networks with interval time-varying delays

The robust asymptotic stability analysis for uncertain BAM neural networks with both interval time-varying delays and stochastic disturbances is considered. By using the stochastic analysis approach, employing some free-weighting matrices and introducing an appropriate type of Lyapunov functional which takes into account the ranges for delays, some new stability criteria are established to guarantee the delayed BAM neural networks to be robustly asymptotically stable in the mean square. Unlike the most existing mean square stability conditions for BAM neural networks, the supplementary requirements that the time derivatives of time-varying delays must be smaller than 1 are released and the lower bounds of time varying delays are not restricted to be 0. Furthermore, in the proposed scheme, the stability conditions are delay-range-dependent and rate-dependent/independent. As a result, the new criteria are applicable to both fast and slow time-varying delays. Three numerical examples are given to illustrate the effectiveness of the proposed criteria.     

New stability criteria for uncertain neural networks with interval time-varying delays

This paper is concerned with the stability analysis for neural networks with interval time-varying delays and parameter uncertainties. An approach combining the Lyapunov-Krasovskii functional with the differential inequality and linear matrix inequality techniques is taken to investigate this problem. By constructing a new Lyapunov-Krasovskii functional and introducing some free weighting matrices, some less conservative delay-derivative-dependent and delay-derivative-independent stability criteria are established in term of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Three numerical examples show that the proposed criterion are effective and is an improvement over some existing results in the literature.     

Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control

This paper investigates drive-response synchronization for a class of neural networks with time-varying discrete and distributed delays (mixed delays) as well as discontinuous activations. Strict mathematical proof shows the global existence of Filippov solutions to neural networks with discontinuous activation functions and the mixed delays. State feedback controller and impulsive controller are designed respectively to guarantee global exponential synchronization of the neural networks. By using Lyapunov function and new analysis techniques, several new synchronization criteria are obtained. Moreover, lower bound on the convergence rate is explicitly estimated when state feedback controller is utilized. Results of this paper are new and some existing ones are extended and improved. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.     

LMI-based asymptotic stability analysis of neural networks with time-varying delays

The problem of the global asymptotic stability for a class of neural networks with time-varying delays is investigated in this paper, where the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By constructing suitable Lyapunov functionals and combining with linear matrix inequality (LMI) technique, new global asymptotic stability criteria about different types of time-varying delays are obtained. It is shown that the criteria can provide less conservative result than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.     

Neural networks in analog hardware--design and implementation issues

This paper presents a brief review of some analog hardware implementations of neural networks. Several criteria for the classification of general neural networks implementations are discussed and a taxonomy induced by these criteria is presented. The paper also discusses some characteristics of analog implementations as well as some trade-offs and issues identified in the work reviewed. Parameters such as precision, chip area, power consumption, speed and noise susceptibility are discussed in the context of neural implementations. A unified review of various "VLSI friendly" algorithms is also presented. The paper concludes with some conclusions drawn from the analysis of the implementations presented.     

具有时滞的Hopfield人工神经网络动力系统模型的全局渐近稳定性

Hopfield人工神经网络动力系统模型平衡点的全局渐近稳定性在网络记忆以及最优化等领域具有广泛的应用。本文中,作者研究了一类具有时滞的Hopfield人工神经网络动力系统,通过构造Liapunov泛函的方法,获得了其平衡点全局渐近稳定和局部渐近稳定的充分判定条件。所给出的判定条件只依赖于系统本身的拳数参数和传递函数以及系统中出现的部分时滞。同时,当系统的自身反馈项为负时,此自身反馈项对于系统的稳定性起到稳定化的作用。此外,数值模拟表明时滞的变化对于系统的稳定性具有重要的影响。可破坏系统的稳定性。进而产生周期振动或更为复杂的非线性现象。     

Delay-decomposing approach to robust stability for switched interval networks with state-dependent switching

This paper is concerned with a class of nonlinear uncertain switched networks with discrete time-varying delays . Based on the strictly complete property of the matrices system and the delay-decomposing approach, exploiting a new Lyapunov–Krasovskii functional decomposing the delays in integral terms, the switching rule depending on the state of the network is designed. Moreover, by piecewise delay method, discussing the Lyapunov functional in every different subintervals, some new delay-dependent robust stability criteria are derived in terms of linear matrix inequalities, which lead to much less conservative results than those in the existing references and improve previous results. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.     

Modeling perceptual learning: difficulties and how they can be overcome

We investigated the roles of feedback and attention in training a vernier discrimination task as an example of perceptual learning. Human learning even of simple stimuli, such as verniers, relies on more complex mechanisms than previously expected – ruling out simple neural network models. These findings are not just an empirical oddity but are evidence that present models fail to reflect some important characteristics of the learning process. We will list some of the problems of neural networks and develop a new model that solves them by incorporating top-down mechanisms. Contrary to neural networks, in our model learning is not driven by the set of stimuli only. Internal estimations of performance and knowledge about the task are also incorporated. Our model implies that under certain conditions the detectability of only some of the stimuli is enhanced while the overall improvement of performance is attributed to a change of decision criteria. An experiment confirms this prediction. Received: 23 May 1996 / Accepted in revised form: 16 October 1997