Skip Navigation


IMA Journal of Applied Mathematics Advance Access originally published online on March 5, 2009
IMA Journal of Applied Mathematics 2009 74(4):559-573; doi:10.1093/imamat/hxp007
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
74/4/559    most recent
hxp007v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Liu, Z.
Right arrow Articles by Tan, R.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Permanence and extinction of an impulsive delay competitive Lotka–Volterra model with periodic coefficients

Zhijun Liu{dagger}

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, People's republic of China and Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei 445000, People's republic of China

Jianhua Wu{ddagger}

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, People's republic of China

Ronghua Tan§

Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei 445000, People's republic of China

{dagger} Corresponding author. Email: zjliu1008{at}gmail.com

{ddagger} Email: jianhuaw{at}snnu.edu.cn

§ Email: ronghua_tan{at}hotmail.com

Received on May 16, 2008; Accepted on January 18, 2009

In this paper, a periodic competitive system with delays and pulses is proposed. By using the comparison theorem for impulsive differential equations and the property of globally asymptotic stability of a periodic single-species growth population model with impulsive perturbations, sufficient conditions for permanence and extinction of the above system are derived, respectively. Our main results show that under appropriate conditions, the permanence and extinction of system are irrespective of the size of delays, however, impulsive perturbations play an important role and have effects on the permanence and extinction of system.

Keywords: permanence; extinction; competitive system; delay; pulse.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.