时滞随机非线性积分微分方程的稳定性分析

发布时间：2018-03-09 08:51

  本文选题：积分微分方程　切入点：时滞随机微分方程　出处：《四川师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文研究一类含时滞的随机非线性积分微分方程的稳定性.寻求研究时滞随机微分方程稳定性的新方法一直以来都是学者们重点关注的对象之一.本文首先建立该类方程的常数变易公式,得出其解的表达形式.其次使用不等式分析技巧,构建恰当的时滞积分不等式和指数型时滞积分不等式.最后使用随机分析理论和不等式分析技巧,借助构建的时滞积分不等式,建立了判别这类时滞的随机非线性积分微分方程的p阶矩稳定、p阶矩渐近稳定、p阶矩一致渐近稳定、p阶矩全局一致渐近稳定、p阶矩指数稳定和p阶矩全局指数稳定性的充分条件(p ≥ 2).文中的举例阐述了时滞积分不等式方法的有效性。
[Abstract]:In this paper, we study the stability of a class of stochastic nonlinear integrodifferential equations with time delay, and seek a new method to study the stability of stochastic differential equations with delay. The constant variable formula of this kind of equation, The expression form of the solution is obtained. Secondly, the appropriate delay integral inequality and exponential delay integral inequality are constructed by using the inequality analysis technique. Finally, the stochastic analysis theory and inequality analysis technique are used. With the help of the time delay integral inequality constructed, In this paper, the p order moment stability and p order moment asymptotic stability of stochastic nonlinear integrodifferential equations with such delays are established, and the global uniform asymptotic stability of p order moment and p order moment exponential stability and p order moment global exponential stability are established. The sufficient condition for qualitative analysis is p 鈮，

本文编号：1587832