tailieunhanh - báo cáo hóa học:" Research Article Note on the Persistent Property of a Discrete Lotka-Volterra Competitive System with Delays and Feedback Controls"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Note on the Persistent Property of a Discrete Lotka-Volterra Competitive System with Delays and Feedback Controls | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 249364 9 pages doi 2010 249364 Research Article Note on the Persistent Property of a Discrete Lotka-Volterra Competitive System with Delays and Feedback Controls Xiangzeng Kong 1 2 Liping Chen 1 2 and Wensheng Yang1 2 1 Key Lab of Network Security and Cryptology Lujian Normal University Fuzhou 350007 China 2 School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China Correspondence should be addressed to Xiangzeng Kong xzkong@ Received 26 June 2010 Accepted 12 September 2010 Academic Editor P. J. Y. Wong Copyright 2010 Xiangzeng Kong et al. 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. A nonautonomous -species discrete Lotka-Volterra competitive system with delays and feedback controls is considered in this work. Sufficient conditions on the coefficients are given to guarantee that all the species are permanent. It is shown that these conditions are weaker than those of Liao et al. 2008. 1. Introduction Traditional Lotka-Volterra competitive systems have been extensively studied by many authors 1-7 .The autonomous model can be expressed as follows N u ff biUi f 1 - atjUj f i 1 . N 1 1 where bi 0 aii 0 aij 0 i f j ui f denoting the density of the ith species at time f. Montes de Oca and Zeeman 6 investigated the general nonautonomous N-species Lotka-Volterra competitive system N u ff Ui f bi f - Cij f Uj t Cij 0 i 1 . N j 1 2 Advances in Difference Equations and obtained that if the coefficients are continuous and bounded above and below by positive constants and if for each i 2 . N there exists an integer k. i such that ị bk i--1 . c i then u. 0 exponentially for 2 i N and . t X where X is a certain solution of a logistic equation. Teng 8 and Ahmad and .