X_ρ空间上随机时滞格系统的随机动力学  

Random Dynamics for Stochastic Delay Lattice Systems in X_ρ Space

作　　者：张一进[1,2] ZHANG Yijin(Chongqing Key Lab of Intelligent Analysis and Decision on Complex Systems,Chongqing University of Postsand Telecommunications,Chongqing 400065,China;Key Laboratory of Industrial Internetof Things and Networked Control,Ministry of Education,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]重庆邮电大学复杂系统智能分析与决策重庆高校重点实验室 [2]重庆邮电大学工业物联网与网络化控制教育部重点实验室

出　　处：《广西师范大学学报（自然科学版）》2019年第3期106-110,共5页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11701060)

摘　　要：本文研究一类加性白噪声驱动的具有时滞的随机格动力系统的动力学。引入Xρ空间,运用Hilbert空间中的基本等式和Young、Gronwall、Schwarz不等式,证明了随机时滞格点方程解的存在性、唯一性和对初值的连续依赖性,从而得到其解生成连续的无穷维随机动力系统。The dynamics of a class of stochastic lattice dynamical systems with time delay driven by additive white noise is studied.Xρspace is introduced,basic equalities,Young inequality,Gronwall inequality and Schwarz inequality are applied.The existence,uniqueness and continuous dependence on the initial data of solutions to the stochastic delay lattice equations with additive noise are presented.Then a continuous infinite dimensional random dynamical system generated by the solutions is obtained.

关 键 词：随机动力系统 时滞方程 格系统 连续依赖性 动力学 

分 类 号：O175.2[理学—数学]