Delay Model for a Cycling Transport Through Porous Medium

A solute transport through a porous medium is examined provided that the fluid leaving the porous sample returns back in a continuous way. The porous medium is thus included into a closed hydrodynamic circuit. This cycling process is suggested as an experimental tool to determine porous medium parameters describing transport. In the present paper the mathematical theory of this method is developed. For the advective type of transport with solute retention and degradation in porous medium, the system of transport equations in a closed circuit is transformed to a delay differential equation. The exact analytical solution to this equation is obtained. The solute concentration manifests both the oscillatory and monotonous behaviors depending on system parameters. The number of oscillation splashes is shown to be always finite. The maximum/minimum points are determined as solutions of a polynomial equation whose degree depends on the unknown solution itself. The cyclic methods to determine porous medium parameters as porosity and retention rate are developed.     

On exponential stability of nonlinear Volterra difference equations in phase spaces

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18 , 909–939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks.     

Functional Differential Equations With Delay and Random Effects

The authors study the existence of mild solutions to a functional differential equation with delay and random effects. They use a random fixed point theorem with a stochastic domain. An example is included to illustrate their results.     

Exponential Behavior of Solutions to Stochastic Integrodifferential Equations with Distributed Delays

In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a C₀-semigroup.     

一类非线性时滞网络控制系统的无源性分析

本文研究了一类非线性时滞网络控制系统的无源性问题.利用Lyapunov稳定性理论,结合线性矩阵不等式(LMI)技术,通过构造Lyapunov-Krasovskii泛函,在考虑两种不同时滞的情况下,获得了系统满足无源性的充分条件,最后通过仿真算例验证了结论的正确性和方法的有效性.     

具有固定时滞的经济周期模型的动态分析

在经济活动中,投资行为和资本存量存在一定的时滞效应,这会影响经济周期模型的动态行为,进而使得投资政策对经济的稳定调整复杂化.考虑到资本存量的预期时间以及投资时滞对经济活动的影响,采用Hopf分岔理论,研究具有固定时滞的经济周期模型的均衡点的稳定性以及形成经济周期的条件.研究发现,投资过程中的投资时滞,以及投资决策中对于资本存量的预测时间构成经济周期产生的诱因;同时可通过政府投资政策调整达到预期均衡目标,这对保持经济周期稳定及经济政策制定有一定的指导作用.     

时间延迟对基因调节回路中生物记忆影响研究

生物记忆是广泛存在于各种生物子系统的一种重要的效应. 基于一个双反馈的基因调节回路模型, 采用数值模拟的方法研究了局部反馈中存在的时间延迟对生物记忆时间的影响. 结果发现, 小量的延迟能够很大地提高生物记忆时间. 并且, 生物记忆随延迟时间呈线性增加. 这种增强模式与噪声对生物记忆时间的提高完全不同. 延迟和噪声对生物记忆的提高可以进行相互的控制增强, 但不会影响对方的增强模式.     

8×8APD阵列激光三维成像接收机研制

为了实现对目标的无扫描阵列激光三维成像并研究系统参数对三维成像距离分辨率的影响,研制了8×8 pixel激光三维成像接收机。接收机采用线性模式APD阵列,设计了模拟信号放大、阈值处理将回波光信号转换为数字信号后,利用FPGA设计实现64通道高精度阵列计时系统,实现了对目标的无扫描实时三维成像功能。首先对设计完成的三维成像接收机组成及成像原理进行了介绍,对三维成像接收机中APD探测器阵列信号的模拟处理和数字处理流程和实现方式进行了说明。随后分别对三维成像的核心FPGA计时系统及探测器整体进行了电子学测试和实验测试。测试结果表明,FPGA计时子系统的时间分辨率优于140 ps,三维成像系统整体距离分辨率在0.2 m左右。最后对分辨率的误差进行了分析,结果表明,激光回波强度波动是影响此接收机距离分辨率的最主要因素。     

Global stability for infinite-delay,dispersive Lotka-Volterra systems: Weakly interacting populations in nearly identical patches

A Lotka-Volterra-like model ofm interacting species which can disperse amongn discrete habitats and where species interaction terms involve general unbounded delays is shown to possess a globally stable equilibrium when the undelayed intraspecific competition term dominates interspecific interactions as well as the delayed intraspecific competition effect and when then habitats are nearly identical.     

SINGULAR PERTURBATION OF INITIAL BOUNDARY VALUE FROBLEMS OF REACTION DIFFUSlON EQUATION WITH DELAY

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