非线性脉冲扰动下带强迫项的次线性时滞微分系统解的渐近性

讨论了带强迫项的次线性时滞微分系统在非线性脉冲扰动下系统解的渐近性,得到了带强迫项的次线性时滞微分系统在非线性脉冲扰动下系统解渐近吸引的充分性条件.     

一类随机脉冲微分系统的稳定性

本文给出了随机脉冲微分系统零解的最终稳定性的定义,利用Liapunov函数,得到了非线性随机脉冲微分系统零解一致最终稳定性及一致最终渐进稳定性和最终不稳定的充分条件.     

一类脉冲微分包含系统的稳定性分析

脉冲微分包含系统是具有状态脉冲的微分包含系统,在建模层面有广泛的模型表征能力.针对一类具有差分包含脉冲形式的线性脉冲微分包含系统,文章探索系统在所有脉冲下的强稳定性,给出基于Lyapunov方法的稳定性判据.特别地,稳定性等价于存在一个联合公共范数,使其对离散子动态诱导出具有压缩性质的公共矩阵范数,及对连续子动态诱导出负值公共测度.该判据可视为连续时间微分包含系统和离散时间差分包含系统相关稳定性判据的完全推广.     

一类交替型脉冲微分系统的解

主要讨论一类超前型与滞后型交替的脉冲微分系统.首先给出具常系数的脉冲微分系统解存在的充分条件以及解唯一的表达形式;对于变系数的微分系统也作了相应的讨论.     

一类脉冲微分系统有界变差解对参数的连续依赖性

文[6]讨论了比已有结果更弱的假设条件下,固定时刻一阶脉冲微分系统与Kurzweil广义常微．分方程的关系,本文在此基础之上,建立了此类脉冲微分系统有界变差解对参数的连续依赖性定理．     

具固定时刻的二阶脉冲微分系统零解的稳定性

利用脉冲微分不等式和分析技巧,构造Lyapunov函数给出了二阶具固定脉冲时刻的微分系统零解的稳定性的两个判定准则,特别突出了脉冲效应对系统稳定性的关键影响,并给出了其相关例子.     

具概率延迟反馈金融系统的脉冲控制

研究了概率时滞脉冲金融系统平衡点的全局渐近稳定性问题。首先,通过定义合适的时滞分段区间上的随机变量,给出了概率时滞的脉冲金融系统的数学模型,根据脉冲微分不等式特点构造了一个简便合适的Lyapunov函数利用脉冲微分不等式引理、控制脉冲间隔与脉冲量以及概率时滞分析技巧,获得了较大时滞允许范畴下的平衡点的全局指数稳定,并通过数值实例验证了方法的可行性以及概率时滞的优势。特别地,稳定性判定准则的时滞允许上限的增大,扩大了准则的实用性.     

具脉冲和时滞影响的非线性抛物系统边值问题的振动结果

研究一类具非线性扩散项的脉冲时滞抛物偏微分系统解的振动性,借助Green公式、垂直相加法和脉冲时滞微分不等式,获得了该类系统在Robin边值条件下振动的充分性条件.所得结果充分反映了脉冲和时滞在系统振动中的影响作用.     

一类脉冲中立型抛物系统振动性

考虑一类具高阶Laplace算子的脉冲中立型抛物偏微分系统的振动性,借助于一阶脉冲时滞微分不等式,得到了该类系统在Dirichlet边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在系统振动中的影响作用.     

具有线性扰动的线性脉冲微分系统的有界增长

本文介绍了脉冲微分系统的有界增长的概念，并进一步讨论了具有线性扰动的线性脉冲微分系统的有界增长问题，得到了反映无扰和扰动两种情形下脉冲微分系统有界增长关系的定理。     

滞后型脉冲泛函微分方程有界性的Lyapunov逆定理

本文通过建立滞后型脉冲泛函微分方程饱和解的存在唯一性定理,在广义常微分方程与滞后型脉冲泛函微分方程等价的基础上,研究了滞后型脉冲泛函微分方程关于一致有界性的Lyapunov逆定理.     

Non-periodic averaging principles for measure functional differential equations and functional dynamic equations on time scales involving impulses

We present a non-periodic averaging principle for measure functional differential equations and, using the correspondence between solutions of measure functional differential equations and solutions of functional dynamic equations on time scales (see Federson et al., 2012 [8]), we obtain a non-periodic averaging result for functional dynamic equations on time scales. Moreover, using the relation between measure functional differential equations and impulsive measure functional differential equations, we get a non-periodic averaging theorem for these equations. Also, it is a known fact that we can relate impulsive measure functional differential equations and impulsive functional dynamic equations on time scales (see Federson et al., 2013 [9]). Therefore, applying this correspondence to our averaging principle, we obtain a non-periodic averaging theorem for impulsive functional dynamic equations on time scales.     

非线性脉冲中立型双曲方程的振动性

讨论非线性时滞脉冲中立型双曲方程的振动性质,利用平均值方法以及泛函微分不等式获得了该类方程在一类非线性边值条件下所有解振动的充分判据.结果表明,振动是由滞量和脉冲引起的.     

高阶脉冲中立型偏泛函微分方程的强迫振动性

研究一类具高阶Laplace算子的高阶脉冲非线性中立型偏泛函微分方程的强迫振动性,利用Green公式和微分不等式方法将所讨论的脉冲中立型偏微分方程转化为脉冲中立型微分不等式的问题,获得了这类方程在三类不同边值条件下所有解强迫振动的若干充分条件.     

Mathematical modelling to control a pest population by infected pests

In this paper, we formulate and investigate the pest control models in accordance with the mathematical theory of epidemiology. We assume that the release of infected pests is continuous and impulsive, respectively. Therefore, our models are the ordinary differential equations and the impulsive differential equations. We study the global stability of the equilibria of the ordinary differential equations. The permanence of the impulsive differential equations is proved. By means of numerical simulation, we obtain the critical values of the control variable under different methods of release of infected pests. Thus, we provide a mathematical evidence in the management of an epidemic controlling a pest.     

Periodic averaging method for impulsive stochastic differential equations with Lévy noise

The purpose of this paper is to present a periodic averaging method for impulsive stochastic differential equations with Lévy noise under non-Lipschitz condition. It is shown that the solutions of impulsive stochastic differential equations with Lévy noise converge to the solutions of the corresponding averaged stochastic differential equations without impulses     

On a class of differential equations of parabolic type with impulsive action

Existence and uniqueness theorems are obtained for semilinear differential equations of parabolic type with impulsive action in Banach spaces. These equations contain an operator, in general, noninvertible, multiplying the time derivative. The results are applied to partial differential equations with impulsive action.     

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.     

Impulsive nonlocal differential equations through differential equations on time scales

We propose a non-standard approach to impulsive differential equations in Banach spaces by embedding this type of problems into differential (dynamic) problems on time scales. We give an existence result for dynamic equations and, as a consequence, we obtain an existence result for impulsive differential equations.     

Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment

This paper intends to develop a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment. By using the theory of impulsive differential equations and stochastic differential equations, we obtain conditions for the extinction and the permanence of the microorganisms of the deterministic chemostat model and the stochastic chemostat model. We develop a new numerical computation method for impulsive stochastic differential system to simulate and illustrate our theoretical conclusions. The biological results show that a small stochastic disturbance can cause the microorganism to die out, that is, a permanent deterministic system can go to extinction under the white noise stochastic disturbance. The theoretical method can also be used to explore the threshold of some impulsive stochastic differential equations.