EXISTENCE, UNIQUENESS AND STABILITY RESULTS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS ON TIME SCALES

被引：0

作者：

Liu, Xinzhi ^{[1
]}

Zhang, Kexue ^{[1
]}

机构：

[1] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada

来源：

DYNAMIC SYSTEMS AND APPLICATIONS | 2016年 / 25卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

EXPONENTIAL STABILITY; DELAY; SYSTEMS; STABILIZATION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies functional differential equations on time scales and develops the theory of existence and uniqueness of solutions by utilizing the induction principle and Gronwall's inequality on time scales. Further more, it establishes several criteria on uniform (asymptotic) stability and exponential stability using Lyapunov functions and Razumikhin technique. These criteria include some known results as special cases. Numerical examples are presented to illustrate the stability criteria.

引用

页码：501 / 529

页数：29

共 26 条

[1]

[Anonymous], 1996, DYNAMIC SYSTEMS MEAS

[2]

[Anonymous], 1988, Ein Ma kettenkalkul mit Anwendung auf Zentrumsmannigfaltigkeiten

[3]

Azbelev N.V., 2007, Introduction to the theory of functional differential equations: methods and applications

[4] Modeling and prediction with a class of time delay dynamic neural networks [J].

Becerikli, Yasar ;

Oysal, Yusuf .

APPLIED SOFT COMPUTING, 2007, 7 (04) :1164-1169

[5]

Bohner M., 2001, Dynamic equations on time scales: an introduction with applications, DOI DOI 10.1007/978-1-4612-0201-1

[6]

Bohner M., 2003, Advances in Dynamic Equations on Time Scales: An Introduction with Applications, DOI DOI 10.1007/978-0-8176-8230-9

[7] BOOLEAN DELAY EQUATIONS ON NETWORKS IN ECONOMICS AND THE GEOSCIENCES [J].

Coluzzi, Barbara ;

Ghil, Michael ;

Hallegatte, Stephane ;

Weisbuch, Gerard .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2011, 21 (12) :3511-3548

[8]

Elaydi S., 1994, FUNKC EKVACIOJ-SER I, V37, P401

[9]

Erneux T., 2009, APPL DELAY DIFFERENC

[10]

Hale J.K., 1977, THEORY FUNCTIONAL DI

← 1 2 3 →