Global exponential stability of interval neural networks with a fixed delay

1.IntroductionConsideradelayedneural-networkmodeldescribedbythefollowingfunctionaldifferentialequations.()()()()()()11,nniiiijjjijjjijjtautwgutvgutImt===-++-+邋&1,2,,.in=K(1a)or()()()()()()ttttt=-++-+uAuWGuVGuI&,(1b)where()()()()T12,,,ntututut=轾臌uListhestatevectoroftheneuralnetwork;()12diag,,,naaa=AKisadiagonalmatrixwithpositiveentries,i.e.,0ia>;()ijnnw=Wand()ijnnv=Varetheconnectionweightmatrixanddelayedconnectionweightmatrix,re-spectively;()()()()()()()()T1122,,,nntgutgutgut轾=臌GuKde…     

Unnatural Disasters: Two Calculus Projects for Instructors Teaching Mathematics for Social Justice

Abstract

We provide context and motivation for an instructor to use real-life examples in the calculus classroom. To this end we describe two specific project ideas, one related to the devastating impact of methylmercury fungicide in a grain seed supply and the other to a catastrophic methane leak. By using calculus in contexts that have social justice implications, we hope to empower students to reason for themselves, to use mathematics as a powerful tool to deepen their understanding of the world, and ultimately, to effectively confront the challenges society faces.     

Hopfield神经网络全局指数稳定性的几个新判据

重新讨论了Hopfield神经网络平衡点的全局指数稳定性，得到了四个新判据，且列举了相应的例子来说明．由这些定理和例题的证明方法，阐述了Lyapunov函数的选择，网络参数电容Ci、电阻Ri及神经元uj(x)的导数ui(x)上下确界Mi，mi，i＝1，2…，n的处理及不等式放缩的精度在构造网络全局指数稳定性判据中的重要性，得到了表明全局指数稳定性收敛速度的Lyapunov指数α的估计式．     

关于Diophantine方程x~3-3~(3m)=Dy~2

设D是无平方因子正奇数.本文证明了:当D不能被6k+1之形素数整除时,如果方程x3-33m=Dy2有适合gcd(x,Y)=1的正整数解(x,y,m),则D≡7(mod 8),D的素因数p都满足了p≡11(mod 12),而且D的素因数个数必为奇数.     

具有多滞后的时变区间动力系统的指数稳定性

引进了多滞后时变区间动力系统的指数稳定的概念，用矩阵测度和时滞微分不等式研究了具有多滞后的时变区间动力系统χ(t)=N[P(t)，Q(t)]χ(t) ∑（i=1，m）N[Pi(t)，Qi(t)]χ(t-τi)，τi0(i=1，2，…，m)的指数稳定性，得到了其指数稳定的一些判据，并给出了应用的例子，改进和推广了前人的工作。     

Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks

The robust exponential stability of a larger class of discrete-time recurrent neural networks (RNNs) is explored in this paper. A novel neural network model, named standard neural network model (SNNM), is introduced to provide a general framework for stability analysis of RNNs. Most of the existing RNNs can be transformed into SNNMs to be analyzed in a unified way. Applying Lyapunov stability theory method and S-Procedure technique, two useful criteria of robust exponential stability for the discrete-time SNNMs are derived. The conditions presented are formulated as linear matrix inequalities (LMIs) to be easily solved using existing efficient convex optimization techniques. An example is presented to demonstrate the transformation procedure and the effectiveness of the results.     

大系统的部分联结一致渐近稳定性及指数稳定性

基于子系统间某些关联可能是固定的情况,本文讨论了大系统的部分联结稳定性,并且利用向量李雅普诺夫函数法研究了大系统的部分联结一致渐近稳定性及指数稳定性,推广了大系统关联稳定性的相关结论。     

Existence and global exponential stability of equilibrium of competitive neural networks with different time scales and multiple delays

In this paper, some sufficient conditions are obtained for existence and global exponential stability of a unique equilibrium point of competitive neural networks with different time scales and multiple delays by using nonlinear Lipschitz measure (NLM) method and constructing suitable Lyapunov functional. The results of this paper are new and they complete previously known results.     

指数波形松弛方法

结合常微分方程的指数方法和波形松弛方法, 建立指数波形松弛方法。然后证明了该方法是收敛的。最后通过算例与显式欧拉方法、指数方法和波形松弛方法进行对比。结果表明,对于弱耦合的大系统, 指数波形松弛方法具有一定优势。     

混合时滞区间神经网络鲁棒指数稳定性

讨论了混合时滞区间神经网络的全局鲁棒指数稳定性．利用拓扑度理论和不等式技巧给出了一个混合时滞区间神经网络平衡点的存在唯一性以及全局鲁棒指数稳定性的条件。