一类具有状态及控制滞后的不确定系统的时滞相关鲁棒H∞控制

讨论了一类同时具有状态时滞与输入时滞的不确定系统的时滞相关鲁棒H∞控制问题．借助于积分不等式，用线性矩阵不等式方法获得了系统时滞相关与时滞导数相关的鲁棒H∞控制器的设计方法．不需要对原系统进行模型变换．     

具时变时滞和无穷时滞及反馈控制的n-种群竞争模型的周期解

研究更为广泛的同时具有交时滞,无穷时滞及反馈控制的n-种群竞争模型,并且以重合度理论和Lyapunov泛函为主要工具,得到了保证模型正周期解存在和全局吸引的充分性条件,所得结论推广了已有结果.     

多重时滞富营养化生态模型的稳定性与分支分析

本文研究了多重时滞富营养化生态模型的稳定性与分支问题.利用特征值方法,分别研究了具有单时滞和双时滞模型的线性稳定性.发现当模型中的时滞经过一系列临界值时,模型在平衡点附近经历了Hopf分支和Hopf-zero分支,并给出Hopf分支和Hopf-zero分支存在的充分条件.最后数值模拟验证了理论结果.     

双时滞HIV病毒的CD4$^+$T-细胞模型的稳定性和分支分析

本文研究双时滞HIV病毒的CD4~+ T-细胞模型.利用特征方程根的分别理论,分别研究具有单时滞和双时滞模型的线性稳定性.发现当模型中的时滞经过一系列临界值时,模型在平衡点经历了Hopf分支和Hopf-zero分支,并给出Hopf分支和Hopf-zero分支存在的充分条件.最后数值模拟验证了理论结果.     

时滞对食物受限种群演化模型的渐近性的影响

该文主要是研究时滞对食物受限的种群演化模型的渐近形态的影响.通过与非时滞系统相比较,得到 了时滞对解的渐近性的影响估计.     

面向混频数据的时滞GM(1,N)模型

采样频率不同、间距不等的混频数据背景下,考虑时滞是系统要素间因果作用的常见现象,提出含时滞参数的混频GM(1,N)建模方法。根据时滞特征不同,将模型划分为两类:同步推移型时滞GM(1,N)模型和累积型时滞GM(1,N)模型。同步推移型用于表征时滞长度固定但起始时间不确定、具有管道延迟性质的时滞关系。累积型用于表征时滞长度不确定、因果效应逐步叠加的时滞关系。将指数Almon函数作为时滞分布函数,该函数可完全由数据驱动生成递增、递减、S型、U型、钟型等多种形态,有助于挖掘混频数据中的时滞信息。数值分析的结果验证了模型的有效性。模型对于存在低频小样本数据的混频时滞系统具有很强的适用性。     

变时滞细胞神经网络稳定性分析

利用矩阵测度、Liapunov函数和Halanay时滞不等式的方法研究了具有变时滞的细胞神经网络模型平衡点的全局指数稳定性问题.给出了判定平衡点全局指数稳定性的几个代数判据,可用于时滞细胞神经网络的设计与检验,数值算例说明其结果的优越性.     

一类带时滞的SIR传染病模型的稳定性

研究了一类带时滞的SIR传染病模型,利用多项式判别系统研究了无病平衡点的全时滞稳定性,利用超越函数零点判别法研究了正平衡点的局部渐近稳定性.     

一类时滞病毒动力学模型的稳定性分析

建立并分析了一类带有两个时滞的病毒动力学模型.通过讨论,获得了有时滞情况下无病平衡点以及正平衡点的稳定性态.     

含有时滞的非线性投资系统模型

在分析投资时滞特征的基础上 ,讨论投资时滞的计算方法 ,给出具有役龄结构并带有时滞的投资系统模型 .     

Blow-up behavior of Hammerstein-type delay Volterra integral equations

We consider the blow-up behavior of Hammerstein-type delay Volterra integral equations (DVIEs). Two types of delays, i.e., vanishing delay (pantograph delay) and non-vanishing delay (constant delay), are considered. With the same assumptions of Volterra integral equations (VIEs), in a similar technology to VIEs, the blow-up conditions of the two types of DVIEs are given. The blow-up behaviors of DVIEs with non-vanishing delay vary with different initial functions and the length of the lag, while DVIEs with pantograph delay own the same blow-up behavior of VIEs. Some examples and applications to delay differential equations illustrate this influence.     

一类中立型退化时滞微分方程的周期解

讨论了一类中立型退化时滞微分方程的周期解的存在条件,并且给出了二维退化滞后微分方程的周期解的存在性问题,且给出了一个充要条件和两个充分条件,最后举例说明结论的有效性。     

Global attractivity in a perturbed linear delay differential equation

In the main result of this paper, some sharp conditions are obtained for global attractivity in a scalar perturbed linear delay differential equation. The proof of the main theorem is based on a new estimate for the infinite integral of the absolute value of the fundamental solution of a linear delay differential equation. We also derive sufficient conditions for asymptotic stability of a system of linear delay differential equations.     

具有时滞的细胞神经网络周期解与稳定性

本文研究了具有时滞的细胞神经网络周期解存在性和平凡解的稳定性问题 .利用 Lyapunov函数法并结合不等式分析技巧 ,我们首先证明了时滞细胞神经网络的解是有界的 ,然后建立了时滞细胞神经网络的周期解的存在准则 ,最后在时滞细胞神经网络有平衡点时 ,给出了神经网络系统的平衡点指数稳定的充分条件 .其结果推广了文 [7,8]的相应结果 .     

不确定时滞Lurie系统的鲁棒绝对稳定性分析

研究了一类不确定Lurie时滞系统的鲁棒绝对稳定性问题，不确定项范数有界。通过构造特殊的李亚普诺夫函数，分别考虑了时滞相关和时滞无关两情况，得到了系统鲁棒绝对稳定的充分条件。     

On the existence and the uniqueness theorem for fractional differential equations with bounded delay within Caputo derivatives

Local and global existence and uniqueness theorems for a functional delay fractional differential equation with bounded delay are investigated. The continuity with respect to the initial function is proved under Lipschitz and the continuity kind conditions are analyzed.     

条件异方差双门限自回归模型的门限和延时的小波估计

本文讨论了条件异方差双门限自回归模型的门限和延时的识别问题,通过经验小波系数,给出了门限个数和门限以及延时的估计,在较弱的条例下,证明了所给的估计是相合的。     

Periodic solutions in periodic state-dependent delay equations and population models

Sufficient and realistic conditions are obtained for the existence of positive periodic solutions in periodic equations with state-dependent delay. The method involves the application of the coincidence degree theorem and estimations of uniform upper bounds on solutions. Applications of these results to some population models are presented. These application results indicate that seasonal effects on population models often lead to synchronous solutions. In addition, we may conclude that when both seasonality and time delay are present and deserve consideration, the seasonality is often the generating force for the often observed oscillatory behavior in population densities.

     

Oscillation of Nonlinear Delay Impulsive Differential Equations and Inequalities

The oscillatory and asymptotic behavior of first-order nonlinear delay impulsive differential equations and inequalities is studied. Some new sharp sufficient conditions for oscillation and nonoscillation of solutions of the equations and inequalities are obtained. Many known results are improved. In particular, the conditions are necessary and sufficient if the equations and inequalities are autonomous.