Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 5, Issue 1, Pages 219-229Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S1468-1218(03)00037-3
Keywords
growth rate; interaction coefficients; persistence; survival; extinction; inequality; linear system
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We consider a nonautonomous competitive Lotka-Volterra system of two species, satisfying two inequalities involving averages of the growth rates and the interaction coefficients, which imply persistence. We introduce a third species and give a third inequality, involving the average of the growth rate of the third species and solutions of a linear algebraic system, which guarantees persistence of the system. It is also shown that reversing this inequality implies non-persistence; more specifically, extinction of the third species with small positive initial values, in the autonomous case. Our conditions are simple and computable. (C) 2003 Elsevier Ltd. All rights reserved.
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