Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 59, Issue 2, Pages 812-828Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2009.10.011
Keywords
Discrete Kolmogorov system; Permanence; Discrete Lyapunov functional; Discrete Lotka-Volterra system; Delay
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Funding
- National Natural Science Foundation of PR China [60764003]
- Scientific Research Programmes of Colleges in Xinjiang [XJEDU2007G01, XJEDU2006I05]
- National Key Technologies R & D Program of China [2008BAI68B01]
- Natural Science Foundation of Jiangxi Province [2008GZS0027]
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In this paper, the permanence for the general nonautonomous n-species discrete Kolmogorov systems with delays is studied. By using the method of multiple discrete Lyapunov-like functionals, a quite general sufficient condition is established. As application of this result, new sufficient conditions are obtained to ensure the permanence of all species for the discrete nonautonomous pure-delayed n-species Lotka-Volterra competitive systems and food chain systems. Particularly, as special cases, a series of new sufficient conditions on the permanence for the discrete nonautonomous pure-delayed Lotka-Volterra two-species competitive systems, predator-prey systems and three-species food chain systems, and the discrete autonomous pure-delayed Lotka-Volterra competition systems and food chain systems are obtained. (C) 2009 Elsevier Ltd. All rights reserved.
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