模糊形态学双向联想记忆网络的性质

为模糊形态学双向联想记忆网络(FMBAM)提出一个学习算法。在理论上证明只要存在使给定的模式对集合成为FMBAM的平衡态集合,则该学习算法总能计算出相应的最大连接权矩阵对。该最大连接权矩阵对能使FMBAM对任意输入在一步内就进入平衡态,并且神经网络全局收敛到平衡态。FMBAM的每个平衡态都是Lyapunov稳定的。当训练模式存在摄动时,利用该学习算法训练的FMBAM,对训练模式摄动拥有好的鲁棒性。     

具有非单调发生率的SIR传染病模型的稳定性

研究了一类具有非单调发生率的SIR传染病模型。给出了系统解的正性、一致有界性和全局吸引性,接着运用Hurwitz-Rouché判别法,讨论了对应系统无病平衡态和地方病平衡态的局部渐近稳定性。最后通过上下解方法和比较原理说明,当常数输入率足够大时,地方病平衡态是全局渐近稳定的;当常数输入率或者接触率足够小时,无病平衡态是全局渐近稳定的。     

一类Holling-Tanner捕食模型的全局稳定性

研究了一类具有扩散项的Holling-Tanner捕食食饵模型,讨论了该模型在齐次Newmann边界条件下正常数平衡解的全局稳定性;并利用比较原理构造上下解的方法,得到了正常数平衡态解全局渐近稳定的条件。     

关于神经网络的能量函数

能量函数在神经网络的研究中有着非常重要的作用,人们普遍认为：只要能量函数沿着网络的解是下降的,能量函数的导数为零的点是网络的平衡态,能量函数有下界,则网络是稳定的且网络的平衡态是能量函数的极小点,文中取反例说明上述条件下不能保证网络的稳定性,并取例说明即使网络稳定也不能保证网络的平衡态与能量函数的极小点,证明了在网络具有上述条件的能量函数的情况下网络稳定的充分必要条件是网络的解有界,讨论了网络的平     

模糊双向联想记忆的稳定性与容错性

证明了基于取大－取小模糊算子对的模糊双向联想记忆网络全局稳定性,并Ｈａｍｍｉｎｇ距离证明了该网络的平衡是Ｌｙａｐｕｎｏｖ稳定的。通过在一定条件下获得的吸引子非退化的吸引域,揭示出网络具有较好的容错性。实例验证了该结论的正确性。     

一类Leslie-Gower捕食-食饵模型的定性分析

研究一类具有Holling-II型反应函数的Leslie-Gower捕食-食饵模型。给出了平衡态方程解的先验估计,讨论了正常数解的局部渐近稳定性和全局渐近稳定性,利用分歧理论,得到了局部分歧解的存在性,最后将局部分歧延拓为全局分歧。     

一个含有扩散的捕食者—食饵—领地生态模型平衡态的稳定性*

本文对含有扩散的捕食者－食饵－领地生态模型进行了讨论，通过构造该系统的不变区域，给出了正整体解存在和有界的范围，同时对其平衡态的稳定性分析提出了一种新的方法－－分域估计法，由此得到了全局渐近稳定的条件。     

带有用户意识的计算机多病毒传播模型

为改进计算机系统及网络的安全性和可信度,提出一种带有用户意识的计算机多病毒传播模型。综合考虑人为因素和客观因素对病毒传播的影响,采用稳定性分析和实验仿真的方法,在理论上证明无病毒平衡态是全局稳定的,地方病平衡态是局部渐进稳定的。实验结果表明,在该模型中,通过提高用户意识可以有效地控制计算机病毒的传播。     

一类竞争模型分歧解的存在性和稳定性

在Dirichlet边界条件下研究了一类具有扩散的两物种竞争模型平衡态正解的存在性和稳定性。运用分歧理论和标准的椭圆型方程正则性理论分析了平衡态分歧解的存在性,得到了其存在的充分条件,并通过数值模拟验证了该条件。利用线性稳定性理论得到了分歧解稳定的条件。研究结果表明,当参数满足一定条件时,系统达到稳定的共存态。     

一类浮游生物捕食系统的全局分歧

主要研究一类在齐次第一边界条件下浮游植物和浮游动物的捕食-食饵模型。给出了平衡态方程解的先验估计。利用分歧理论,以b为分歧参数,得到平衡态系统正解的存在性,将局部分歧延拓为全局分歧。结果表明连通分支C延伸向无穷。     

Equilibrium Analysis for Improved Signal Range Model of Delayed Cellular Neural Networks

In this paper, a class of delayed cellular neural networks with unbounded activation functions and described by using space invariant cloning templates are considered. The general and explicit existing regions of equilibrium points are discussed based on dissipative theory, fixed point principle of iteration mapping and Brouwer Fixed-point Theorem. The sufficient condition is obtained to ensure the existence, uniqueness, local asymptotical stability of the equilibrium point in each saturation sub-region. Moreover, we give the condition for equilibrium point to be globally exponentially stable, and the explicit existing region of the unique equilibrium point is also located. These results extend previous works on these issues for the standard delayed cellular neural networks. Two numerical examples are given to show the validity of the obtained results.     

Global aspects of the matrix Riccati equation

Matrix Riccati equations are interpreted as differential equations on Grassman manifolds. Necessary conditions for the Riccati equation to be a Morse-Smale system are given in the autonomous and periodic cases. Under this condition, the equation is structurally stable and has a unique asymptotically stable equilibrium point or periodic solution.     

具有漏泄时滞的高阶细胞神经网络的多周期性分析

分析了一类具有漏泄时滞的高阶细胞神经网络的多周期性和指数收敛性. 给出了保证此类网络的周期环在饱和区内局部指数收敛的充分条件. 所得结果表明, 一个n维网络可以有2^n个周期环存在于饱和区, 而且这些周期环是局部指数收敛的. 仿真实例进一步证明了结论的有效性.     

具漏泄时滞的细胞神经网络多周期性分析

针对一类具有漏泄时滞细胞神经网络模型,首先给出该类网络的周期环在饱和区局部指数收敛的充分条件.研究表明,一个n维网络可以有2n个周期环存在于饱和区,并且这些周期环是局部指数收敛的.然后,研究了该时滞细胞神经网络指数周期的一个特殊情形--指数稳定.数值例子和仿真结果验证了所得结果的有效性.     

Global exponential stability of neural networks with globallyLipschitz continuous activations and its application to linearvariational inequality problem

This paper investigates the existence, uniqueness, and global exponential stability (GES) of the equilibrium point for a large class of neural networks with globally Lipschitz continuous activations including the widely used sigmoidal activations and the piecewise linear activations. The provided sufficient condition for GES is mild and some conditions easily examined in practice are also presented. The GES of neural networks in the case of locally Lipschitz continuous activations is also obtained under an appropriate condition. The analysis results given in the paper extend substantially the existing relevant stability results in the literature, and therefore expand significantly the application range of neural networks in solving optimization problems. As a demonstration, we apply the obtained analysis results to the design of a recurrent neural network (RNN) for solving the linear variational inequality problem (VIP) defined on any nonempty and closed box set, which includes the box constrained quadratic programming and the linear complementarity problem as the special cases. It can be inferred that the linear VIP has a unique solution for the class of Lyapunov diagonally stable matrices, and that the synthesized RNN is globally exponentially convergent to the unique solution. Some illustrative simulation examples are also given.     

Existence and Global Exponential Stability of Periodic Solution for a Class of Neutral-Type Neural Networks with Time Delays

This paper is concerned with the problems of existence and stability of the periodic solution for a class of neutral-type neural networks. The neural network addressed is general where the time delays and difference operator are taken into account. By employing the Mawhin’s continuation theorem, the sufficient condition is obtained to guarantee the existence and uniqueness of the periodic solution for the neutral-type neural networks. By constructing a novel Lyapunov functional, a unified framework is established to derive sufficient conditions for the concerned system to be globally exponentially stable. A numerical example is provided to demonstrate the usefulness of the main results obtained.     

一类高阶Cohen-Grossberg神经网络的多周期性分析

利用状态空间分解方法,探讨一类具有特殊激励函数的高阶Ｃｏｈｅｎ-Ｇｒｏｓｓｂｅｒｇ神经网络的多周期性问题．该类神经网络的激励函数包括带有饱和区的非递减函数以及一般的细胞神经网络激励函数等．给出了保证此类网络的周期环在饱和区内局部指数收敛的充分条件．所得结果表明,一个狀维网络可以有２ⁿ个局部指数收敛的周期环存在于饱和区．最后以一个数值例子说明了所得结果的有效性．     

Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions

This paper investigates the global asymptotic stability of the periodic solution for a general class of neural networks whose neuron activation functions are modeled by discontinuous functions with linear growth property. By using Leray-Schauder alternative theorem, the existence of the periodic solution is proved. Based on the matrix theory and generalized Lyapunov approach, a sufficient condition which ensures the global asymptotical stability of a unique periodic solution is presented. The obtained results can be applied to check the global asymptotical stability of discontinuous neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also conform the validity of Forti’s conjecture for discontinuous neural networks with linear growth activation functions. Two illustrative examples are given to demonstrate the effectiveness of the present results.     

离散Hopfield双向联想记忆神经网络的稳定性分析

首先将离散Hopfield双向联想记忆神经网络转化成一个特殊的离散Hopfield网络 模型.在此基础上,对离散Hopfield双向联想记忆神经网络的全局渐近稳定性和全局指数稳 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的而且是渐近 稳定的平衡点.利用Lyapunov方程正对角解的存在性得到了几个判定平衡点为全局渐近稳 定和全局指数稳定的充分条件.这些条件可以用于设计全局渐近稳定和全局指数稳定的神经 网络.所做的分析扩展了以前的稳定性结果.     

A competitive associative memory model and its dynamics

Conventional associative memory networks perform "noncompetitive recognition" or "competitive recognition in distance". In this paper a "competitive recognition" associative memory model is introduced which simulates the competitive persistence of biological species. Unlike most of the conventional networks, the proposed model takes only the prototype patterns as its equilibrium points, so that the spurious points are effectively excluded. Furthermore, it is shown that, as the competitive parameters vary, the network has a unique stable equilibrium point corresponding to the winner competitive parameter and, in this case, the unique stable equilibrium state can be recalled from any initial key.