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研究了一类G-Brown运动驱动的中立型随机时滞微分方程的指数稳定性.在G-框架意义下,运用合适的Lyapunov-Krasovskii泛函,中立型时滞微分方程理论以及随机分析技巧,证明了所研究方程平凡解的p-阶矩指数稳定性,得到了所研究方程平凡解是p-阶矩指数稳定的充分条件.最后通过例子说明所得的结果. 相似文献
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本文考虑马尔可夫调制中立型随机时滞微分方程,利用比较原理研究其依概率稳定及依概率一致稳定。 相似文献
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吴晓蕾 《数学的实践与认识》2021,(10):240-246
研究一类具有泊松跳的中立型随机时滞微分方程.首先应用Lyapunov-Krasovskii泛函以及Dynkin's公式讨论模型平凡解的p阶矩稳定性问题.接着给出实例验证理论结果的有效性. 相似文献
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退化时滞中立型微分系统的特征根分布与指数稳定 总被引:3,自引:2,他引:1
本文首先讨论了两类具有一般意义的线性自治中立型时滞微分系统特征根链的分布情况,并且给出特征根链的逼近链拟合曲线,然后重点讨论多时滞退化中立型微分系统的特征根链分布,由此得到多时滞退化中立型微分系统指数稳定的条件. 相似文献
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本文首先在Lipschiz条件和线性增长条件下,通过Picard迭代法研究了带跳的无限时滞中立型随机微分方程解的存在唯一性,接着对这这类方程的Picard迭代解与精确解的误差进行估计,最后讨论了解的矩估计。 相似文献
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本文使用一类新方法研究中立型随机泛函微分方程的均方指数稳定性.由此,一些新的关于所考虑的方程解的均方指数稳定性结果被获得,一些已有的结果被改进.最后通过分析一些实例阐述了我们获得的理论的有效性. 相似文献
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本文考虑含扰动项的具有正负系数的中立型泛函微分方程一致稳定和渐近稳定的充分条件,推广了现有文献中的结论. 相似文献
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具有正负系数的中立型时滞微分方程 总被引:21,自引:1,他引:21
考虑具有正负系数的中立型时滞微分方程d/dt[x(t)-C(t)x(t-r)]+P(t)x(t-r)-Q(t)x(t-δ)=0(1)我们获得了(1)的所有解振动的“sharp”条件,即条件在系数C(t),P(t)及Q(t)为常数时是充分必要的.作为其推论也大大地推广并改进了文[2—5,7—9]的相应定理. 相似文献
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The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching. 相似文献
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In this paper,by constructing proper Lyapunov functions,exponential stability criteria for stochastic delay partial differential equations are obtained. An example is shown to illustrate the results. 相似文献
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This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations. 相似文献
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In this paper, we study two types of neutral functional differential equations with finite or unbounded distributed deviating arguments. By Banach contraction princi-ple, we obtain some sufficient conditions for the existence of positive solutions to such equations. 相似文献
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Oscillation criteria for the delay differential equationx′(t)+p(t)x(t-т(t))=0,where p, т are non-negative real-valued continuous functions are investigated inthe case when the numbers k=integral from n=t-т(t) to t(p(s)ds),L=integral from n=t-т(t) to t(p(s)ds)satisfy 0≤k<1/e and 1/e≤L<1. The present result improves almost allresults of the literature concerning it. Furthermore, it is established that allsolutions of the odd-order neutral delay differential equation(x(t)-px(t-т))~(n)+Q(t)x(t-σ)=0,where 0≤p<1,т,σ∈(0,∞)and Q(t)≥0,are oscillatory ifintegral from n=t-σ to t ((t-s)~(n-1)Q(s)ds>(1/e)(1-p)(n-1))!.This result generalizes a theorem of Gopalsamy et. al (Czech. Math. J., 42(1992),313-323)and also extends a very well-known result of Ladas (ApplicableAnalysls, 9(1979),93-98). 相似文献
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本文讨论Euler方法用于求解线性中立型随机延迟微分方程初值问题时数值解的稳定性,利用了一种不同于以往文献中的证明技巧,给出了Euler方法均方稳定的一个充分条件.文末的数值试验证实了本文所获理论结果的正确性. 相似文献
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In this paper,we study one type of odd-order neutral delay differential equation. Suffcient conditions for the oscillation of every solution to this type of differential equation are given. 相似文献