带阈值的Min—max模糊Hopfield网络的稳定性与容错性分析

本文讨论了带阈值的Ｍｉｎ－ｍａｘ模糊Ｈｏｐｆｉｅｌｄ网络的性质，并研究了该网络的一致稳定性与平衡态的Ｌｙａｐｕｎｏｖ稳定性。给出了一个模糊模式成为该网络吸引子的等价条件。然后在一定的条件下，得到了这个网络吸引子的一个非退化的吸引域，从而我们所建立的模糊神经网络模型具有较强的容错性，最后的例子证实了这一点。     

具有随机时延的模糊不确定网络控制系统的指数镇定

研究了一类非线性不确定网络系统的指数镇定问题.根据网络诱导时延在不同区间上取值,引入满足Bernoulli分布的随机变量,建立新的非线性网络系统模型.利用Lyapunov稳定性理论,以线性矩阵不等式形式给出系统均方指数镇定条件和模糊控制器设计策略.仿真算例说明了方法的有效性.     

单种群阶段结构的生育脉冲模型

本文研究单种群阶段结构生育脉冲的数学模型,通过研究其频闪映射所确定的离散动力系统,我们获得了生育脉冲的系统存在周期解及其稳定的阈值,阐述了阈值的生物意义.     

一类具有两阶段结构的自治SIS传染病系统

讨论了具有两阶段结构的自治SIS传染病系统,证明了该系统的边界平衡态和正平衡态的全局渐近稳定性,得到了使其渐近稳定的阈值.     

基于GA-BP的锅炉燃烧系统的仿真与研究

在当今社会中,我国的发电仍然以火力发电为主.锅炉能否安全经济的燃烧是火力发电厂最为关心的问题.锅炉安全经济的燃烧不仅可以使得发电成本降低还能有效的减少有害物质的排放.依据某热电厂的现场数据选用BP神经网络来对锅炉燃烧系统进行建模分析.利用遗传算法对BP神经网络的权值、阈值进行优化,建立更为理想的GA-BP网络模型.实验结果表明,在采用遗传算法优化的神经网络之后,模型的收敛速度、训练精度得到了有效的提高.为了进一步的研究该系统,建立模糊PID优化控制器并仿真,仿真结果证明了模糊PID的优越性.以上研究说明,通过以上手段可以有效地优化热电厂的锅炉燃烧系统.     

基于模糊双线性模型的非线性系统的跟踪控制

研究一种基于T-S模糊双线性系统的跟踪控制器设计及稳定性分析.使用分布并行补偿法(PDC)设计了模糊控制器,得到模糊双线性系统跟踪控制渐近稳定的充分条件,仿真结果验证了该方法改进了闭环系统的性能.     

一种基于神经元的自适应模糊推理网络

本文根据Ｔ－Ｓ模糊模型提出了一种新的基于神经元的自适应模糊推理网络，给出了连接结构和学习算法，它能自动学习和修正隶属函数及模糊规则，将其用于Ｂｏｘ的煤气炉，太阳黑子预报以及降雨量预报等不同类型的复杂系统建模，仿真结果表明，该模糊神经网络具有收敛速度快，辨识精度高，泛化能力强和适应范围广等特点，可当作复杂系统建模的一种有效工具。     

具有密度依赖的生育脉冲单种群阶段结构模型

给出具有密度依赖生育脉冲单种群阶段结构数学模型．通过研究其频闪映射所确定的离散动力系统,获得了具有生育脉冲的系统存在周期解及其稳定的阈值,当系统的参数超过阈值,存在一系列的分支并最终走向混沌,这说明生育脉冲使系统动力学行为变得非常复杂,提供了一个自然的周期,而使系统从倍周期分支到混沌．     

基于犹豫模糊相似的网络正能量推荐算法研究

论文依据网络正能量模糊性和多规则的特点,借助语言犹豫模糊集和普通犹豫模糊集建立正能量事件的评价集,针对事件属性对正能量的影响效应确定各属性的模糊熵和权重,建立犹豫模糊推荐模型。借助TOPSIS的思想,从大数据中得到正能量事件的标准值,通过事件与标准值模糊相似度的计算确定推荐阈值以得到满意的正能量事件推荐结果。     

具有线性脉冲的周期捕食系统的持久性

研究具有HollingIV功能性反应和脉冲的周期捕食食饵系统．找到了影响该系统动力学行为的阈值Ro．证明了当Ro〈1时,该系统的食饵灭绝周期解是局部渐近稳定的;当R0〉1时,该系统的食饵灭绝周期解变得不稳定且食饵将一致持久．     

Stability Analysis of Gradient-Based Neural Networks for Optimization Problems

The paper introduces a new approach to analyze the stability of neural network models without using any Lyapunov function. With the new approach, we investigate the stability properties of the general gradient-based neural network model for optimization problems. Our discussion includes both isolated equilibrium points and connected equilibrium sets which could be unbounded. For a general optimization problem, if the objective function is bounded below and its gradient is Lipschitz continuous, we prove that (a) any trajectory of the gradient-based neural network converges to an equilibrium point, and (b) the Lyapunov stability is equivalent to the asymptotical stability in the gradient-based neural networks. For a convex optimization problem, under the same assumptions, we show that any trajectory of gradient-based neural networks will converge to an asymptotically stable equilibrium point of the neural networks. For a general nonlinear objective function, we propose a refined gradient-based neural network, whose trajectory with any arbitrary initial point will converge to an equilibrium point, which satisfies the second order necessary optimality conditions for optimization problems. Promising simulation results of a refined gradient-based neural network on some problems are also reported.     

Stability of the LCD model

The growing network model with loops and multiple edges proposed by Bollobás et al. (Random Structures and Algorithms 18(2001)) is restudied from another perspective. Based on the first-passage probability of Markov chains, we prove that the degree distribution of the LCD model is power-law with degree exponent 3 as the network size grows to infinity.     

A characterization of stochastically stable networks

Jackson and Watts (J Econ Theory 71: 44–74, 2002) have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, p-pairwise stability, which allows us to characterize the stochastically stable networks without requiring the “tree construction” and the computation of resistance that may be quite complex. When a -pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of p-pairwise stable networks, we define its set-valued extension with the notion of p-pairwise stable set. The -pairwise stable set exists and is unique. Any stochastically stable networks is included in the -pairwise stable set. Thus, any network outside the -pairwise stable set must be considered as a non-robust network. We also show that the -pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more “stable” than a pairwise stable network.     

一类分数阶神经网络模型的稳定性与Hopf分支分析

分析了一类分数阶神经网络的稳定性与Hopf分支问题.基于分数阶稳定性判据,得到了分数阶神经网络模型局部渐近稳定的条件.并以q为分支参数,得到了分数阶系统产生Hopf的条件.最后数值仿真证明了我们的结论.     

时滞离散网络模型的动力学分析与同步

复杂网络广泛存在于日常生活,首先,给出几类标准的网络模型;然后,利用稳定性控制方法设计并实现了具有时滞与非时滞耦合的复杂网络模型快速控制;最后,通过构造优化Lyapunov函数,讨论其模型的射影同步问题,得到了系统全局稳定的条件和有效的控制器,以实例数值验证其方法的可行性。     

Convergence Dynamics of Delayed Hopfield-Type Neural Networks Under Almost Periodic Stimuli

Convergence dynamics of Hopfield-type neural networks subjected to almost periodic external stimuli are investigated. In this article, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures. By employing Halanay inequalities, we obtain delay independent sufficient conditions for the networks to converge exponentially toward encoded patterns associated with the external stimuli. The networks are guaranteed to have exponentially hetero-associative stable encoding of the external stimuli.     

Existence and Exponential Stability of Almost Periodic Solution for Hopfield Neural Network Equations with Almost Periodic Imput

By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. In this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.     

一类分数阶Hopfield神经网络的鲁棒指数稳定性

本文研究了一类具有Caputo导数的分数阶Hopfield神经网络的鲁棒指数稳定性, 得到了保证其鲁棒指数稳定性的一些充分条件. 最后利用数值仿真验证了结论的正确性和有效性.     

A characterisation of (max,+)-linear queueing systems

The (max,+)-algebra has been successfully applied to many areas of queueing theory, like stability analysis and ergodic theory. These results are mainly based on two ingredients: (1) a (max,+)-linear model of the time dynamic of the system under consideration, and (2) the time-invariance of the structure of the (max,+)-model. Unfortunately, (max,+)-linearity is a purely algebraic concept and it is by no means immediate if a queueing network admits a (max,+)-linear representation satisfying (1) and (2). In this paper we derive the condition a queueing network must meet if it is to have a (max,+)-linear representation. In particular, we study (max,+)-linear systems with time-invariant transition structures. For this class of systems, we find a surprisingly simple necessary and sufficient condition for (max,+)-linearity, based on the flow of customers through the network. This revised version was published online in June 2006 with corrections to the Cover Date.     

星形热弹性网络系统的稳定性及Riesz基性质

研究了一类星形弹性网络系统在热效应影响以及边界反馈作用下的稳定性问题及系统相应（广义）特征向量的Riesz基性质．基于Green和Naghdi第二类热弹性理论,假设在该热弹性系统中热以有限波速传播,并且在传播过程中无能量耗散．证明了该热弹性网络系统能量渐近衰减到零．并进一步通过系统算子谱分析,讨论得出该系统算子的（广义）特征向量构成状态空间的一组Riesz基．