A new method for exponential stability of coupled reaction-diffusion systems with mixed delays: Combining Razumikhin method with graph theory

Wenxue Li; Xiaoqing Zhang; Chunmei Zhang

doi:10.1016/j.jfranklin.2014.12.012

A new method for exponential stability of coupled reaction-diffusion systems with mixed delays: Combining Razumikhin method with graph theory

Wenxue Li^*
, Xiaoqing Zhang
, Chunmei Zhang

^*Corresponding author for this work

Harbin Institute of Technology Weihai
University of Illinois at Urbana-Champaign

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

This paper is concerned with a new method for exponential stability of coupled reaction-diffusion systems with mixed delays (CRDSMD). In CRDSMD, the features of reaction-diffusion systems and mixed delays systems are both taken into account. Based on the Razumikhin method and graph theory, several stability conditions are presented, including the Razumikhin-type theorem, the Lyapunov-type theorem and a sufficient criterion in the form of coefficient. As a subsequent result, the coupled reaction-diffusion systems with discrete time-varying delay are also discussed, and a sufficient criterion in the form of coefficient is given to determine its exponential stability. Finally, a numerical example is provided to illustrate the effectiveness of the results developed.

Original language	English
Pages (from-to)	1169-1191
Number of pages	23
Journal	Journal of the Franklin Institute
Volume	352
Issue number	3
DOIs	https://doi.org/10.1016/j.jfranklin.2014.12.012
State	Published - 1 Mar 2015
Externally published	Yes

Access to Document

10.1016/j.jfranklin.2014.12.012

Cite this

@article{7bf9dcc008334f81a97a1ca982bb9091,

title = "A new method for exponential stability of coupled reaction-diffusion systems with mixed delays: Combining Razumikhin method with graph theory",

abstract = "This paper is concerned with a new method for exponential stability of coupled reaction-diffusion systems with mixed delays (CRDSMD). In CRDSMD, the features of reaction-diffusion systems and mixed delays systems are both taken into account. Based on the Razumikhin method and graph theory, several stability conditions are presented, including the Razumikhin-type theorem, the Lyapunov-type theorem and a sufficient criterion in the form of coefficient. As a subsequent result, the coupled reaction-diffusion systems with discrete time-varying delay are also discussed, and a sufficient criterion in the form of coefficient is given to determine its exponential stability. Finally, a numerical example is provided to illustrate the effectiveness of the results developed.",

author = "Wenxue Li and Xiaoqing Zhang and Chunmei Zhang",

note = "Publisher Copyright: {\textcopyright} 2015 The Franklin Institute.",

year = "2015",

month = mar,

day = "1",

doi = "10.1016/j.jfranklin.2014.12.012",

language = "英语",

volume = "352",

pages = "1169--1191",

journal = "Journal of the Franklin Institute",

issn = "0016-0032",

publisher = "Elsevier Ltd",

number = "3",

}

TY - JOUR

T1 - A new method for exponential stability of coupled reaction-diffusion systems with mixed delays

T2 - Combining Razumikhin method with graph theory

AU - Li, Wenxue

AU - Zhang, Xiaoqing

AU - Zhang, Chunmei

PY - 2015/3/1

Y1 - 2015/3/1

N2 - This paper is concerned with a new method for exponential stability of coupled reaction-diffusion systems with mixed delays (CRDSMD). In CRDSMD, the features of reaction-diffusion systems and mixed delays systems are both taken into account. Based on the Razumikhin method and graph theory, several stability conditions are presented, including the Razumikhin-type theorem, the Lyapunov-type theorem and a sufficient criterion in the form of coefficient. As a subsequent result, the coupled reaction-diffusion systems with discrete time-varying delay are also discussed, and a sufficient criterion in the form of coefficient is given to determine its exponential stability. Finally, a numerical example is provided to illustrate the effectiveness of the results developed.

AB - This paper is concerned with a new method for exponential stability of coupled reaction-diffusion systems with mixed delays (CRDSMD). In CRDSMD, the features of reaction-diffusion systems and mixed delays systems are both taken into account. Based on the Razumikhin method and graph theory, several stability conditions are presented, including the Razumikhin-type theorem, the Lyapunov-type theorem and a sufficient criterion in the form of coefficient. As a subsequent result, the coupled reaction-diffusion systems with discrete time-varying delay are also discussed, and a sufficient criterion in the form of coefficient is given to determine its exponential stability. Finally, a numerical example is provided to illustrate the effectiveness of the results developed.

UR - https://www.scopus.com/pages/publications/84922961104

U2 - 10.1016/j.jfranklin.2014.12.012

DO - 10.1016/j.jfranklin.2014.12.012

M3 - 文章

AN - SCOPUS:84922961104

SN - 0016-0032

VL - 352

SP - 1169

EP - 1191

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 3

ER -

A new method for exponential stability of coupled reaction-diffusion systems with mixed delays: Combining Razumikhin method with graph theory

Abstract

Access to Document

Other files and links

Fingerprint

Cite this