多变时滞Volterra型动力系统的稳定性  

Stability of Volterra Type Dynamic Systems with Time-Varying Delays

作　　者：王春生[1] 李永明[2] WANG Chun-sheng;LI Yong-ming(Department of Management,South China Institute of Software Engineering,Guangzhou University,Guangzhou 510990,China;School of Mathematics & Computer Science,Shangrao Normal University,Shangrao Jiangxi 334001,China)

机构地区：[1]广州大学华软软件学院管理系,广州510990 [2]上饶师范学院数学与计算机科学学院,江西上饶334001

出　　处：《西南大学学报（自然科学版）》2019年第7期62-69,共8页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11461057);广东省普通高校特色创新项目(自然科学)(2018KTSCX339);广州大学华软软件学院科学研究、教育教学研究项目(ky201801)

摘　　要：探讨了一类多变时滞积分微分动力系统,并通过不动点方法给出了该系统零解渐近稳定的充要条件.在构造算子时,根据动力系统时滞特点,分别引入对应的连续函数hi(s),i=1,2,…,n,然后利用这n个函数来构造算子,最后再利用Banach不动点方法来研究该动力系统的稳定性.In this paper, a class of dynamic Integro differential dynamical systems with time-varying delays is discussed. The necessary and sufficient conditions for the asymptotic stability of the zero solution of the system are obtained by using the fixed point method. Some continuous functions hi(s), i=1,2,…,n are introduced according to the characteristics of the dynamic system with delays, and then these functions are used to construct the operator. Finally, the Banach fixed point method is used to study the stability of the dynamic system.

关 键 词：Banach不动点 渐近稳定性 多变时滞 Volterra型动力系统 

分 类 号：O231.3[理学—运筹学与控制论]