Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 299, Issue 2, Pages 663-675Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2004.06.019
Keywords
Lotka-Volterra system; permanence; extinction; lower average; upper average
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An n species nonautonomous competitive Lotka-Volterra system is considered in this paper. The average conditions on the coefficients are given to guarantee that all but one of the species are driven to extinction. The generalization for the result is presented, that is, for each r less than or equal to n the average conditions on the coefficients are provided to guarantee that r of the species in the system are permanent while the remaining n - r are driven to extinction. It is shown that these average conditions are improvement of those of Ahmad and Montes de Oca [Appl. Math. Comput. 90 (1998) 155-166] and Montes de Oca and Zeeman [Proc. Amer. Math. Soc. 124 (1996) 3677-3687] and [J. Math. Anal. Appl. 192 (1995) 360-370]. (C) 2004 Elsevier Inc. All rights reserved.
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