摘要
研究了下列非线性pantograph混合随机微分方程dx(t)=f(x(t),x(θ1t),t,r(t))dt+g(x(t),x(θ2t),t,r(t))dB(t),t≥0的零解的指数稳定性.利用随机微分方程的相关理论与M-矩阵理论,得到方程的零解的渐近有界性、p-阶指数稳定、几乎必然指数稳定和H∞稳定.推广了已有文献中的相关结论.
The exponential stability of the trivial solution of the following nonlinear pantograph hybrid stochastic differential equation dx(t)=f(x(t),x(θ1t),t,r(t))dt+g(x(t),x(θ2t),t,r(t))dB(t),t≥0 is discussed.By using the corresponding theory of stochastic differential equations and M- matrices theory,asymptotic boundedness,pth moment exponential stability and H∞ stability of the trival solution of the above equation are obtained.These criteria have generalized the corresponding results in some existing papers.
作者
刘变红
袁志宏
刘桂荣
LIU Bian-hong;YUAN Zhi-hong;LIU Gui-rong(Department of Mathematics,College of Lvliang ,Lvliang033000,China;School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)
出处
《数学的实践与认识》
北大核心
2018年第24期266-272,共7页
Mathematics in Practice and Theory
基金
国家自然科学资金(11471197)
动态重叠网络上疾病和信息传播动力学建模与分析
