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

共 31 条

[1]

[Anonymous], 1967, DIFFERENTIAL EQUATIO

[2]

Aubin J.-P., 1990, Systems & Control: Foundations & Applications, V2

[3]

Aubin Jean-Pierre, 1984, FUNDAMENTAL PRINCIPL, V264

[4]

Benchohra M., 2001, ELECT J DIFFERENTIAL, P8

[5]

Berman A., 1979, COMPUTER SCI APPL MA

[6]

Bernfeld S.R., 1990, SIAM Rev., V32, P312, DOI [10.1137/1032060, DOI 10.1137/1032060]

[7] Existence of periodic and non-periodic solutions to systems of boundary value problems for first-order differential inclusions with super-linear growth [J].

Boucherif, Abdelkader ;

Tisdell, Christopher C. .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 204 (01) :441-449

[8]

Cortés J, 2008, IEEE CONTR SYST MAG, V28, P36, DOI 10.1109/MCS.2008.919306

[9] Topological degree and periodic solutions of differential inclusions [J].

de Blasi, FS ;

Górniewicz, L ;

Pianigini, G .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 37 (02) :217-243

[10] Fixed-point theorems for discontinuous multivalued operators on ordered spaces with applications [J].

Dhage, BC .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 51 (3-4) :589-604

← 1 2 3 4 →