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.     

脉冲泛函微分方程的渐近性态

该文讨论脉冲泛函微分方程$\left\{\begin{array}{ll}x^,(t)=f(t,x_t), t≥ t₀,△x=I_k(t,x(t^-)), t=t_k,k∈ Z⁺,给出了方程零解渐近稳定性和一致渐近稳定性的充分条件,指出这些条件推广或改进了文献[7--9]的相应结论.     

一类脉冲微分系统的有界变差解

在比文[6]更弱的条件下讨论了固定时刻脉冲微分系统与Kurzweil广义常微分方程的关系,并建立了这类脉冲微分系统有界变差解的局部存在性和唯一性定理．     

Existence of Global Solutions for a Class of Abstract Second-Order Nonlocal Cauchy Problem with Impulsive Conditions in Banach Spaces

In this paper, we are concerned with a class of abstract second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces. First, we study the existence of mild solutions for a class of second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces on an interval [0,a]. Later, we study a couple of cases where we can establish the existence of global solutions for a class of abstract second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces. We apply our theory to study the existence of solutions for impulsive partial differential equations.     

一类二阶非线性脉冲时滞微分方程的振动性

考虑一类二阶非线性脉冲时滞微分方程,得到了方程所有解振动的两个充分条件,推广了D■urina和Stavroulakis[Appl Math Comput,2003,140,445—453]中关于非脉冲方程的相关结果.     

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．     

具有脉冲扰动的宏观经济模型及稳定性分析

针对我国经济发展的特点,分析了国民经济运行的脉动机理,建立了一个具有脉冲影响的数学模型;利用李雅谱诺夫函数对系统的平衡点进行了定性分析,得到了系统稳定的判别条件.运用所得结果对我国经济波动的机理以及未来影响我国经济波动的因素进行了分析.     

二阶非线性脉冲时滞微分方程的振动性

利用广义黎卡提变换得到了一类二阶非线性脉冲时滞微分方程所有解振动的充分条件,推广了Dz∨urina和Stavroulakis中关于非脉冲方程的相关结果.     

T-S模糊系统的脉冲稳定性

针对模糊控制系统提出了一种新的稳定性设计方法.该方法在传统T-S模型的局部子系统中引入脉冲控制项,构造了具有脉冲影响的模糊控制系统.然后,通过去模糊化技术,把具有脉冲影响的模糊系统转化为脉冲微分系统.这样,借助脉冲微分方程的比较原理和线性矩阵不等式技术,给出了模糊系统的脉冲稳定的充分条件.从而建立了模糊系统的简单脉冲控制策略.     

Integral boundary value problems for nonlinear non-instantaneous impulsive differential equations

In this paper, we study integral boundary value problems for two classes of nonlinear non-instantaneous impulsive ordinary differential equations. More precisely, one is integer order impulsive model, the other is fractional order impulsive model. By using standard fixed point approach, a series of existence results are presented under different conditions.     

具非线性传染率与生物化学控制的害虫管理S-I模型

讨论了具有非线性传染率与脉冲控制的害虫管理S-I传染病模型,此模型考虑的是脉冲投放病虫和喷洒农药.不但得到了系统的所有解的一致完全有界,而且得到了害虫灭绝的边界周期解的全局渐进稳定和系统的一致持久的条件.为实际的害虫管理提供了可靠的理论依据.     

THE PERIODIC BOUNDARY PROBLE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH VARIABLE TIME

1 IntroductionIt is well known that the monotonic iterative technique is a successfulmethod to obtain the extremal solutions of ODE or IDE with fixed time (see[IJ, [2]). Some results about the monotonic iterative technique for IDE withvariable time were obtained in the past few years (see [3--7]). Because thetheory of IDE with variable time is more complicated than that of IDE withfixed time, many authors considered the special case in which the pulse surfacet = T(x) is strictly monoton…     

Global exponential stability of a class of retarded impulsive differential equations with applications

This paper studies the dynamics of a class of retarded impulsive differential equations (IDE), which generalizes the delayed cellular neural networks (DCNN), delayed bidirectional associative memory (BAM) neural networks and some population growth models. Some sufficient criteria are obtained for the existence and global exponential stability of a unique equilibrium. When the impulsive jumps are absent, our results reduce to its corresponding results for the non-impulsive systems. The approaches are based on Banach’s fixed point theorem, matrix theory and its spectral theory. Due to this method, our results generalize and improve many previous known results such as [3], [5], [6], [9], [17], [18], [23], [32], [38], [43], [51], [52]. Some examples are also included to illustrate the feasibility and effectiveness of the results obtained.     

An impulsive controlled eco-epidemic model with disease in the prey

In this paper, we investigate the dynamic behavior of an eco-epidemic model with impulsive control strategy. By using Floquet theorem of impulsive differential equation, we show there is a globally stable prey eradication periodic solution when the impulsive period is less than some critical value. We study the permanence of the system. Numerical simulations show that the complex dynamics of the system depends on the values of impulsive period and impulsive perturbation, for example double period, triple period solutions.     

On Existence of Solution, Oscillatory and Non-Oscillatory Properties of Delay Impulsive Differential Equations Containing ‘Maximum’

In this paper, we determined the criteria for the existence of solutions for delay impulsive differential equations containing ‘maximum’ (DIDEM) using the Morales’ fixed point theorem. An impulsive analogue of the Gronwall-Bellman’s inequality with deviating argument is also considered. Some results on the oscillation and non-oscillation of solutions of the (DIDEM) are also obtained. Applications of the oscillatory results obtained are made to four non-linear examples one of which is a military model and upper bounds found for the solutions of the impulsive Fitzhugh-Naguno model and an impulsive nonlinear control system.     

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.     

非线性接触率SIR模型脉冲接种策略研究

建立了具有非线性接触率脉冲预防接种的SIR传染病模型,利用脉冲微分方程理论,对模型的动力学性态进行了分析,给出了模型的阀值,证明了无病周期解的存在性及全局渐近稳定性.     

Threshold dynamics of a stage-structured single population model with non-transient and transient impulsive effects

In this paper, we present a stage-structured single population model with non-transient and transient impulsive effects. By the stroboscopic map theories of impulsive differential equations, we obtain the sufficient conditions for the permanence of the investigated system. The results indicate that the thresholds of the transient impulsive harvesting amount and the non-transient impulsive harvesting interval play important roles on the permanence of population. Our results also provide reliable tactic basis for the practical biological resource management.     

Impulsive systems and their applications

A brief survey is made of impulsive systems. In particular, models such as population of a species in a given ecosystem under rapid changes and the impulsive analogue of simple epidemiological model are considered and results confirming the general broadness of impulsive systems over ordinary differential equations are discussed.     

PRACTICAL STABILITY OF DYNAMIC SYSTEMS WITH IMPULISIVE SOLUTIONS

ＰＲＡＣＴＩＣＡＬＳＴＡＢＩＬＩＴＹＯＦＤＹＮＡＭＩＣＳＹＳＴＥＭＳＷＩＴＨＩＭＰＵＬＩＳＩＶＥＳＯＬＵＴＩＯＮＳＨｅＪｉａｎｘｕｎ（贺建勋）（ＸｉａｍｅｎＵｎｉｖｅｒｓｉｔｙ，厦门大学，邮编：３６１００５）Ａｂｓｔｒａｃｔ：Ｐｒａｃｔｉｃａｌｓｔａ...