Robust stability for stochastic interval delayed Hopfield neural networks

A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) WIf(t,u(t)) WIτf7τ(uτ(t)] dt σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.     

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

This paper considers the Rosenau equation with a moving control?t u + ?_t?_x~4 u + ?_xu + u?x u = a(x + ct)h(x, t), c = 0, x ∈ T = R/(2πZ), t 0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in H~s(T) with s ≥ 2. The two results nontrivially extend the work of(Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.     

SOME INITIAL-OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS WITH UNBOUNDED COEFFICIENTS

1 IntroductionThis paper is concerned with the a priori estimates and the ekistence of solutions of theinitiaLoblique derivative boundary value problem for quasilinear non-divergence parabolic equa-tions as follows:where O is a bounded domain in R"(N > 2) with smooth boundary 0a e C' ', QT =[o,T) x a be the parabolic domain in H" ,, ST = [o,T) x aa is the lateral boundary, andarQT is the parabolic boundary of QT' The repeated indices means summatiOns from 1 to N.In [11, the first bounda…     

ASYMPTOTIC STABILITY OF VISCOUS SHOCK PROFILE FOR NON-CONVEX SYSTEM OF ONE-DIMENSIONAL VISCOELASTIC MATERIALS WITH BOUNDARY EFFECT

1 IntroductionWe consider the system of one-dimensiona1 viscoelastic materials with non--convekity of thefOrm.with the illitial-boundary conditionshere v is the strain, u is the ve1ocity p > 0 is the viscous constallt, v and u are givenconstants, a is the pressure to be a known smooth fUnction of v satisfying the fOllOwing signconditions:a'(v) > 0 fOr all v u-nder consideration, (1.4)a"(v) 2 0 fOr v 2 0 under consideration, (l.5)so that rr(v) has a point of inflection at v = 0. We see that…     

Forced Oscillations of a Class of Nonlinear Dispersive Wave Equations and their Stability

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Korteweg-de Vries （KdV） equation and the damped Benjamin-Bona-Mahony （BBM） equation. In this paper we intend to show the same results hold for the pure KdV equation （without the damping terms） posed on a finite domain. Consideration is given to the initial-boundary-value problem {ut＋ux＋uux＋uxxx=0, u（x,0）=φ（x）, 0〈x〈1, t〉0,u（0,t）=h（t）, u（1,t） = 0, ux（1,t） = 0, t〉0.It is shown that if the boundary forcing h is periodic with small ampitude, then the small amplitude solution u of （＊） becomes eventually time-periodic. Viewing （＊） （without the initial condition） as an infinite-dimensional dynamical system in the Hilbert space L^2（0, 1）, we also demonstrate that for a given periodic boundary forcing with small amplitude, the system （＊） admits a （locally） unique limit cycle, or forced oscillation, which is locally exponentially stable. A list of open problems are included for the interested readers to conduct further investigations.     

UPPER AND LOWER SOLUTIONS METHODS FOR EXISTENCE OF PERIODIC SOLUTIONS OF DUFFING EQUATION

1.IntroductionandNotationsInthispapertwestudytheexistenceofsolutionstothefollowingperiodicboundaryvalueproblemforthesecondorderDuffingequationwheresisarealparameter,g:[0,TIxR~RisaCarath6odoryfunctionandkER\{0}.Werecall(forexample,see[1])thatg:[0,TIxR~RiscalledaCarath6odoryfunctionifg(.,x)ismeasurableforallxERandg(t,.)iscontinuousfora.e.tE[0,TI.Theexistenceproblemfor(1.1)--(1.2)byusingtheupperandlowersolutionsmethodhasbeenstudiedbyFabryetal.in[2]foramoregeneralcasewhereacontinuousdampin…     

APPLICATIONS OF INTEGRATED SEMIGROUPS TO HIGHER ORDER ABSTRACT CAUCHY PROBLEMS

This paper is concerned with applications of integrated semigroups tothe following Cauchy problem:(ACP_n) x~(n)(t)=sum from i=0 to n-1 B_ix~(i)(t),x~(i)(0)=x_i,0(?)i(?)n-1where B_i (0(?)i(?)n-1) are closed linear operators on a Banach space X.Auniqueness theorem,a condition of the solvability,a condition of the exponentialwell-posedness,and some results for the special case that B_(n-1) is bounded andD(B_(n-2))(?)D(B_i)(0(?)i(?)n-3) are obtained.     

均衡函数及其在变权综合中的应用

进一步研究了均衡函数，改进了［４］中公理化体系，获得了两大数均衡函数及相应的变权模式并分析了这些模式之间的关系。     

FURTHER RESULTS ON THE ASYMPTOTIC BEHAVIOUR OF MINIMUM AVERAGE HAMMING DISTANCE FOR BINARY CODES

1.IntroductionLetFZnbethen-dimensionalvectorspaceoverthebinaryfieldF2.Anon-emptysubsetACFZniscalledacode.TheaverageHa~ngdistanceofacodeAisdefinedby1\d(A)=IAIz,ZZdH(x,y)ahApeAwhereIAIisthenUmberofcodewordsinA,dH(x,y)istheHammingdistancebetweenxandy.ForallaE{1,2,'',2"}andn21,wedefinetheminimumaverageHammingdistanceasda(a)=^.gle^l=.d(A).AlilswedeandAlthofer[1]provedthefollowingtheorem.Theorem1illLetan(15anS2"),n=1,2,'',beasequenceOjpositiveintegers.Ijforsomeconstanto(0相似文献   

FINITE DIMENSIONAL BEHAVIOR FOR THE DISSIPATIVE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATIONS

This paper deals with the asymptotic behaviour of solutions for the generalized symmetric regularized long wave equations with dissipation term. We first show the existence of global weak attractors for the periodic initial value problem of this equations in H2 x H1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the global weak attractor is actually the global strong attractor for S(t) in H2(2) x H1(M).The finite dimensionality of the global attractor is also established.     

When Research and Practice Collide: The Role of Action Research When There Is a Conflict of Interest with Stakeholders

This article discusses problematic aspects of the role of the action researcher when working with multiple stakeholders on a complex research project concerning regional development. The case presented here deals with the improvement of the regional innovation system in a small region in the south of Norway. The project resulted in a conflict between stakeholders and the action research (AR) team. We claim that when working in a regional context, the role of the action researcher is set to be a collaborator in a context of power play; the ultimate stakeholders must be defined as the citizens in that region. Therefore, in some situations the action researcher must have a legitimatised right to abandon collaboration and present a critical voice in the public deliberation. Strategic power play and strategic action by stakeholders represent a clear threat to the soft approach of collaboration, reflectivity, and democratic dialogue that AR represents. The ultimate challenge and obligation of the action researcher is to improve democracy in society in a long-term perspective through representing a critical capacity in the public deliberation.     

一般Levy过程下带违约风险的可转换债券定价模型

对可转换债券的相应标的股价S_t=S_0exp[(r-q)t+X_t],在X_t是Levy过程的假设下,运用傅立叶变换和残数定理,得出了带有赎回和回售条款的可转换债券的定价公式;同时,结合Duffie关于衍生产品带违约风险的定价方法,给出了带违约风险的可转换债券定价公式.     

ON A FINITENESS THEOREM ABOUT PROBLEMS INVOLVING INEQUALITIES

ＯＮＡＦＩＮＩＴＥＮＥＳＳＴＨＥＯＲＥＭＡＢＯＵＴＰＲＯＢＬＥＭＳＩＮＶＯＬＶＩＮＧＩＮＥＱＵＡＬＩＴＩＥＳ￥ＷＵＷｅｎｉｎｎ（ＷＵＷｅｎ－ｔｓｕｎ）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１...     

Distributed Parameter Neural Networks via Adaptive Wavelet

The paper outlines a new neural net (DPNN) for describing brain's action based on one-dimensional cable theory. While the traditional neural network system only finding its character involving time changing (as HNN, BP etc.), the model-DPNNs (distributed parameter neural networks) are not only the transmitted neurons of time variation, but also the functions of positions by the voltage u(x. I). With the neuroscientific relevance, some bionural features like intermittent conduction and dendritic spike are fixed well by DPNNs which considered as complicated and adaptive devices contract to the functional elementary units. To find the semi-analytical representation of DPNNs, adaptive wavelets are utilized as new microlocalization tools. While maintaining all advantages of wavelet function, the adaptive wavelet offers a viable alternative learning procedure to the orthogonal least squares method (OLS), Adaptive wavelet method develops a fairly general, low-cost multiscale method for neural net optimization.     

舆论演化的社会影响级联效应模型

舆论建模跳出传统的基于最近邻("person-person")的交互范式,引入次近邻("personperson-person")的影响,刻画网络中邻居的邻居对观点改变的作用,提出舆论演化的社会影响级联模型,分析其在可变聚类系数网络上舆论的演化性质.通过调节网络聚类系数,使用异步更新的方式,观察网络集聚特性对舆论演化的影响.结果表明,1)相比于传统的最近邻影响模型,社会影响级联模型的社会强化作用更大,系统更容易达成共识,初始状态中主流观点的影响将被放大;2)舆论演化结果与网络集聚性和初始状态相关:当系统初始状态p_+≠p_,系统观点演化达到稳态后,网络聚类系数越大,越容易产生主流观点;当初始观点p_+=p_时,即正、负力量势均力敌时,系统共识则难以确定.这种情况和现实社会舆论的演化结果符合.     

惯导系统陀螺漂移的ESO估计算法

为满足舰艇航行的高精度导航要求,提高惯导系统陀螺漂移估计精度,设计了基于扩张状态观测器(extended state observer, ESO)的惯导系统陀螺漂移估计算法。首先引入了惯导系统水平姿态角的ESO估计算法;其次基于惯导系统姿态控制方程,研究并推导了陀螺漂移的ESO估计算法,给出了估计误差的量化分析结论;最后对算法进行了仿真验证。结果表明,基于ESO的陀螺漂移估计方法可在短时间内快速、无超调、高精度地估计出陀螺漂移,当ΔAx=ΔAy=10^-5g时,估计的稳态误差约为10^-4(°)/h,提高了惯导系统后续导航精度。     

基于扩张状态观测器的航天器时延状态反馈控制

研究了刚性航天器的时延姿态稳定控制问题。首先建立了基于修正罗德里格斯参数(modified rodrigues parameters, MRPs)的航天器非线性状态模型,具有确定上界的时延项在状态反馈控制律中体现。通过构造Lyapunov Krasovskii 泛函进行稳定性分析,由此得到保证系统渐近稳定的线性矩阵不等式,依此设计状态反馈控制系数矩阵。考虑到航天器三轴间的耦合非线性项,利用扩张状态观测器(extended state observer, ESO) 方法,设计了二阶非线性扩张状态观测器,以获得航天器系统内部状态向量并用于状态反馈控制律。为便于工程实际应用,仿真中将MRPs响应输出转换为欧拉角响应,仿真结果表明,本文所设计的控制系统能保证航天器三轴姿态稳定。     

Some New Results for M/G/1 and GI/G/1 Queues

ＳｏｍｅＮｅｗＲｅｓｕｌｔｓｆｏｒＭ／Ｇ／１ａｎｄＧＩ／Ｇ／１ＱｕｅｕｅｓＴＡＮＧＹｉｎｇｈｕｉ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＥｌｅｃｔｒｏｎｉｃＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙｏｆＣ...     

市场经济:模糊可拓控制与协商决策支持系统

本文利用 F推理和 F转移矩阵对市场经济信息进行了可拓分析 ,并根据实际情况确定关联函数 Ku(x) .当 Ku(x) >0属于传统控制论 ,非线性时用模糊控制 ;当 0 >Ku (x) >-1时属于可拓控制 ;当 -1 >Ku(x) >-∞时实行模糊可拓控制 ,或协商控制 .给出计算机程序框图 ,并对各个框图进行了较详细的解释 ,特别对可拓协商控制理论 ,作了较详细的探讨.     

基于径向基函数网络或模糊系统的非线性连续时间系统的自适应调节

对于一类连续时间的非线性动态系统x=f(x)+Bu+d,当系统中的非线性函数f(x)满足有界或线性增长条件(具有未知的增长系数)时,首先证明了f(x)中的x落入一紧集中,然后根据径向基函数网络或模糊系统的逼近性质,给出了两种自适应调节器的设计方法.利用李亚普诺夫稳定性理论,证明了控制算法是全局稳定的,闭环系统的状态是一致最终有界的,且控制律是稳定的.