Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 710353, 15 pages
doi:10.1155/2009/710353
Research Article

Global Dynamics of Discrete Competitive Models with Large Intrinsic Growth Rates

Chunqing Wu1,2 and Jing-an Cui1

1School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, China
2Department of Information Science, Jiangsu Polytechnic University, Changzhou 213164, China

Received 15 May 2009; Accepted 27 June 2009

Academic Editor: Yong Zhou

Copyright © 2009 Chunqing Wu and Jing-an Cui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The global dynamics of discrete competitive model of Lotka-Volterra type with two species is considered. Earlier works have shown that the unique positive equilibrium is globally attractive under the assumption that the intrinsic growth rates of the two competitive species are less than 1+ln 2, and further the unique positive equilibrium is globally asymptotically stable under the stronger condition that the intrinsic growth rates of the two competitive species are less than or equal to 1. We prove that the system can also be globally asymptotically stable when the intrinsic growth rates of the two competitive species are greater than 1 and globally attractive when the intrinsic growth rates of the two competitive species are greater than 1 + ln 2.