PERIODIC ORBIT ANALYSIS FOR THE DELAYED FILIPPOV SYSTEM

被引：83

作者：

Cai, Zuowei ^{[1
]}

Huang, Jianhua ^{[2
]}

Huang, Lihong ^{[3
]}

机构：

[1] Hunan Womens Univ, Dept Informat Technol, Changsha 410002, Hunan, Peoples R China

[2] Natl Univ Def Technol, Coll Sci, Changsha 410073, Hunan, Peoples R China

[3] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 11期

基金：

中国博士后科学基金;

关键词：

Delayed differential inclusions; Filippov solution; periodic solution; neural networks; FUNCTIONAL-DIFFERENTIAL INCLUSIONS; INTEGRAL INCLUSIONS; EXISTENCE; EQUATIONS; THEOREM;

D O I：

10.1090/proc/13883

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a general class of the delayed differential equation with a discontinuous right-hand side is considered. Under the extended Filippov differential inclusions framework, some new criteria are obtained to guarantee the existence of a periodic solution by employing Kakutani's fixed point theorem of set-valued maps and matrix theory. Then, we apply these criteria to the time-delayed neural networks with discontinuous neuron activations. Our analysis method and theoretical results are of great significance in the design of time-delayed neural network circuits with discontinuous neuron activation under a periodic environment.

引用

页码：4667 / 4682

页数：16

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