时标动力方程的稳定性分析

近来,一种称之为时标动力系统的新理论得到了蓬勃的发展. 该文给出并建立了时标动力系统的各种稳定性概念和Lyapunov稳定性准则(稳定, 一致稳定, 渐近稳定, 指数渐近稳定等等).     

Stability of Viscoelastic Wave Equation with Structural δ-Evolution in R^n

The aim of this paper is to study the Cauchy problem for the viscoelastic wave equation for structuralδ-evolution models.By using the energy method in the Fourier spaces,we obtain the decay estimates of the solution to considered problem.     

GLOBAL EXPONENTIAL STABILITY IN HOPFIELD AND BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH TIME DELAYS

Without assuming the boundedness, strict monotonicity and differentiability of the activation functions, the authors utilize the Lyapunov functional method to analyze the global convergence of some delayed models. For the Hopfield neural network with time delays, a new sufficient condition ensuring the existence, uniqueness and global exponential stability of the equilibrium point is derived. This criterion concerning the signs of entries in the connection matrix imposes constraints on the feedback matrix independently of the delay parameters. From a new viewpoint, the bidirectional associative memory neural network with time delays is investigated and a new global exponential stability result is given.     

具有反应扩散项的变时滞复数域神经网络的指数稳定性

该文研究了一类具有反应扩散项的变时滞复数域神经网络的指数稳定性.首先在假设复数域激活函数可分解的情况下,将该系统分解为相应的实部系统和虚部系统.利用矢量Lyapunov函数法和M矩阵理论,得到了确保该系统平衡状态指数稳定性的充分条件.该条件不含有任何自由变量,相对现有结论具有较低的保守性.最后通过一个数值仿真算例验证了所得结论的正确性.     

一类三阶时滞微分方程解的渐进稳定性

本文研究了三阶非线性时滞微分方程解的渐近稳定性.利用Lyapunov泛函,得到了微分方程的零解是渐进稳定的,这一结果推广了文献[2]的结果.     

Traveling Waves of a Reaction-Diffusion SIRQ Epidemic Model with Relapse

This paper is concerned with the traveling waves of a reaction-diffusion SIRQ epidemic model with relapse. We find that the existence and nonexistence of traveling waves are determined by the basic reproduction number of the system and the minimal wave speed. This threshold dynamics is proved by Schauder''s fixed-point theorem combining Lyapunov functional with the theory of asymptotic spreading. Moreover, the numerical simulations are provided to illustrate our analytical results and the effect of the relapse is also discussed.     

多孔材料分形扩散模型的Fourier-Bessel级数算法及其应用

将Fick扩散定律的Fourier三角级数算法推广成多孔材料分形扩散模型的Fourier-Bessel级数算法,并把它应用于化学工程中吸附问题涉及的浓度分布与相对吸附量的计算中,取得一些规律性认识.由于分形扩散模型是在Fick扩散定律的基础上增加了表征微观结构的参数d_f和θ,研究多孔材料中的浓度分布与相对吸附量时,与Fick扩散定律的研究结果相比,定性上基本一致,在定量上有差别,d_f和θ对扩散传质过程的影响各有侧重,用它们可更好地描述多孔材料中的扩散过程.     

Projective synchronization of spatiotemporal chaos in a weighted complex network

<正>Projective synchronization of a weighted complex network is studied in which nodes are spatiotemporal chaos systems and all nodes are coupled not with the nonlinear terms of the system but through a weighted connection.The range of the linear coefficient matrix of separated configuration,when the synchronization is implemented,is determined according to Lyapunov stability theory.It is found that projective synchronization can be realized for unidirectional star-connection even if the coupling strength between the nodes is a given arbitrary weight value.The Gray-Scott models having spatiotemporal chaos behaviours are taken as nodes in the weighted complex network,and simulation results of spatiotemporal synchronization show the effectiveness of the method.     

Adaptive synchronization of a critical chaotic system

This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory, a novel adaptive control law is derived for the synchronization of a new chaotic system with known or unknown system parameters. Theoretical analysis and numerical simulations show the effectiveness and feasibility of the proposed schemes.     

Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.