脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.     

脉冲中立型时滞微分方程的振动性

本文证明了线性脉冲中立型微分方程解的振动性等价于一类线性非脉冲中立型时滞微分方程解的振动性.应用这一结果,建立了线性脉冲中立型方程解振动性的显式判据.这些判别条件,显著地改进了已有的结果.     

脉冲中立型时滞微分方程的振动性

本文证明了线性脉冲中立型微分方程解的振动性等价于一类线性非脉冲中立型时滞微分方程解的振动性．应用这一结果,建立了线性脉冲中立型方程解振动性的显式判据．这些判别条件,显著地改进了已有的结果．     

脉冲中立型时滞微分方程的振动性

证明了线性脉冲中立型时滞微分方程解的振动性等价于一类非脉冲中立型时滞微分方程解的振动性,应用这一结果建立了此类线性脉冲中立型微分方程解的振动性的显示判据。     

具有连续变量的多时滞二阶中立型差分方程的振动准则

本文用分析的方法研究了一类具有连续变量的多时滞二阶中立型差分方程解的振动性，给出了该类方程解振动和差分算子振动的几个充分条件．     

高阶中立型时滞差分方程解的振动性

研究了一类具有变系数的高阶中立型时滞差分方程解的振动性，给出了其有界解振动的两个充分条件。     

一类二阶中立型泛函微分方程的振动性

讨论了一类二阶中立型微分方程的振动性 ,通过引入参数函数 ,结合完全平方技术 ,给出了该类方程解振动的更为一般形式的判别准则 .     

脉冲向量中立型抛物方程解的H-振动性

研究一类脉冲向量中立型抛物偏微分方程边值问题解的振动性,利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维脉冲中立型微分不等式正解的不存在性问题,并借助于一阶脉冲中立型微分不等式,给出了该类边值问题所有解H-振动的若干充分性判据,这里H是R~M中的单位向量.     

一类二阶中立型方程的振动准则

本文建立了一类二阶中立型方程解的振动准则.     

一类二阶中立型方程的振动准则

本建立了一类二阶中立型方程解的振动准则。     

Oscillation and other properties of linear impulsive and nonimpulsive delay equations

Many of the oscillation results for linear impulsive equations were justified by the following scheme. First, the equivalence of the oscillation of the impulsive equation and some specially constructed nonimpulsive equation was established; further, on the base of well-known results for the nonimpulsive case, the oscillation of the impulsive equation was analyzed. In the present paper, we prove the “oscillation equivalence” result for a linear impulsive equation with a distributed delay and discuss the possibility to expand this approach to the other properties of impulsive equations, for example, stability and asymptotic behavior. In addition, a linear impulsive equation of the second order is considered.     

Oscillation behavior of solution of impulsive fractional differential equation

In this paper, we study the oscillation of impulsive Caputo fractional differential equation. Sufficient conditions for the asymptotic and oscillation of the equation are obtained by using the inequality principle and Bihari Lemma. An example is given to illustrate the results. This is the first time to study the oscillation of impulsive fractional differential equation with Caputo derivative.     

Oscillation and stability of nonlinear neutral impulsive delay differential equations

In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equation are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.     

里卡蒂方法研究带泛函参数的非线性脉冲时滞双曲方程的振动性

本文研究了带泛函参数的非线性脉冲时滞双曲方程的振动性问题.利用积分平均法和里卡蒂方法得到了这类方程解的振动性的一个充分条件,对非线性时滞双曲方程解的震动性进行了推广,能更好地利用一些现有的脉冲时滞常微分方程解的振动性的结论.     

The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy

In this paper, by using theories and methods of ecology and ordinary differential equation, the dynamics complexity of a prey–predator system with Beddington-type functional response and impulsive control strategy is established. Conditions for the system to be extinct are given by using the Floquet theory of impulsive equation and small amplitude perturbation skills. Furthermore, by using the method of numerical simulation with the international software Maple, the influence of the impulsive perturbations on the inherent oscillation is investigated, which shows rich dynamics, such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, period doubling bifurcation, symmetry-breaking pitchfork bifurcation, period-halving bifurcation and crises, etc. The numerical results indicate that computer simulation is a useful method for studying the complex dynamic systems.     

The dynamics of a Beddington-type system with impulsive control strategy

In this paper, by using the theories and methods of ecology and ordinary differential equation, a prey–predator system with Beddington-type functional response and impulsive control strategy is established. Conditions for the system to be extinct are given by using the theories of impulsive equation and small amplitude perturbation skills. It is proved that the system is permanent via the method of comparison involving multiple Liapunov functions. Furthermore, by using the method of numerical simulation, the influence of the impulsive control strategy on the inherent oscillation are investigated, which shows rich dynamics, such as period doubling bifurcation, crises, symmetry-breaking pitchfork bifurcations, chaotic bands, quasi-periodic oscillation, narrow periodic window, wide periodic window, period-halving bifurcation, etc. That will be useful for study of the dynamic complexity of ecosystems.     

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.     

脉冲时滞抛物型方程解的振动准则

本文研究含脉冲的时滞抛物型方程解的振动性,在两类不同边界条件下得到了若干解的振动准则．     

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.     

含变时滞脉冲差分方程解的振动性

本文讨论含变时滞脉冲差分方程解的振动性,获得了方程所有解振动的充分条件.