Exponential stability of singularly perturbed impulsive delay differential equations

In this paper, the exponential stability of singularly perturbed impulsive delay differential equations (SPIDDEs) is concerned. We first establish a delay differential inequality, which is useful to deal with the stability of SPIDDEs, and then by the obtained inequality, a sufficient condition is provided to ensure that any solution of SPIDDEs is exponentially stable for sufficiently small ε>0. A numerical example and the simulation result show the effectiveness of our theoretical result.     

Linear system model for planar concave grating demultiplexer

A linear system model for planar concave grating demultiplexer is developed based on the scalar diffraction theory. With this model the system can be simulated by using Fourier transform. Many device performances such as dispersion features, N × N interconnection, channel uniformity, insertion loss, crosstalk can be estimated or optimized. Furthermore, the behavior of aberration is included in the generalized model.     

关于稳定性的几个基本定理

本文给出了非自治常微分方程稳定性，一致稳定性，渐近稳定性与一致渐近稳定性的几个定理。这些定理允许Lyapunov函数的导数为变号函数，放宽了Marachkov定理对系统状态变量变化率有界的要求，推广了文[4-7]的相应结果。     

Impulsive delay differential inequality and stability of neural networks

In this article, a generalized model of neural networks involving time-varying delays and impulses is considered. By establishing the delay differential inequality with impulsive initial conditions and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, some new sufficient conditions for global exponential stability of impulsive delay model are obtained. The results extend and improve the earlier publications. An example is given to illustrate the theory.     

Banach空间上泛函微分方程的渐近性

§ 1　IntroductionIn the last few years,invariant sets and attractors of (functional) differentialequations have been extensively discussed and various interesting results on the invariantsets and attractors,and estimates on the basin of attraction have been reported(see,forinstance,[1 ,2 ,4,6,1 0 ,1 3 ,1 5,1 8] ) .However,not much hasbeen developed in the directionof giving criteria on the existence of invariant sets and attractors for the functionaldifferential equations even though there ar…     

量子控制论在化学中的应用

控制量子现象是化学研究中的一个重要目标,量子控制论对实现该目标具有积极的指导意义.本文综述了量子控制论在化学中的应用及其进展,重点分析了量子相干控制、量子优化控制、闭环学习控制和能控性观念在化学研究中的应用,介绍了它们的研究现状,并对其未来研究进行了展望.     

Existence-uniqueness and continuation theorems for stochastic functional differential equations

The main aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs). Firstly, we establish stochastic versions of the well-known Picard local existence-uniqueness theorem given by Driver and continuation theorems given by Hale and Driver for functional differential equations (FDEs). Then, we extend the global existence-uniqueness theorems of Wintner for ordinary differential equations (ODEs), Driver for FDEs and Taniguchi for stochastic ordinary differential equations (SODEs) to SFDEs. These show clearly the power of our new results.     

Existence and exponential stability of periodic solution for impulsive delay differential equations and applications

In this paper, we consider a class of nonlinear impulsive delay differential equations. By establishing an exponential estimate for delay differential inequality with impulsive initial condition and employing Banach fixed point theorem, we obtain several sufficient conditions ensuring the existence, uniqueness and global exponential stability of a periodic solution for nonlinear impulsive delay differential equations. Furthermore, the criteria are applied to analyze dynamical behavior of impulsive delay Hopfield neural networks and the results show different behavior of impulsive system originating from one continuous system.     

MULTIPLE PERIODICITY TO A CLASS OF DELAYED STATE-DEPENDENT PREDATOR-PREY SYSTEM

The existence of the multiple positive periodic solutions to a delayed state- dependent predator-prey system with non-monotonic functional response is con- sidered.Using the continuation theorem based on Mawhin's coincidence degree, some more generalized results are obtained.