Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays

Abstract and Applied Analysis. 2012;2012 DOI 10.1155/2012/210156

 

Journal Homepage

Journal Title: Abstract and Applied Analysis

ISSN: 1085-3375 (Print); 1687-0409 (Online)

Publisher: Hindawi Publishing Corporation

LCC Subject Category: Science: Mathematics

Country of publisher: Egypt

Language of fulltext: English

Full-text formats available: PDF, HTML, ePUB, XML

 

AUTHORS

T. S. Doan (Department of Mathematics, Imperial College London, London SW7 2AZ, UK)
S. Siegmund (Center for Dynamics, TU Dresden, 01062 Dresden, Germany)

EDITORIAL INFORMATION

Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 27 weeks

 

Abstract | Full Text

We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.