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Extinction of species in nonautonomous Lotka-Volterra systems


Author: Shair Ahmad
Journal: Proc. Amer. Math. Soc. 127 (1999), 2905-2910
MSC (1991): Primary 34C35; Secondary 34D05
DOI: https://doi.org/10.1090/S0002-9939-99-05083-2
Published electronically: April 23, 1999
MathSciNet review: 1636914
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Abstract: A nonautonomous $n$th order Lotka-Volterra system of differential equations is considered. It is shown that if the coefficients satisfy certain inequalities, then any solution with positive components at some point will have all of its last $n-1$ components tend to zero, while the first one will stabilize at a certain solution of a logistic equation.


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Additional Information

Shair Ahmad
Affiliation: Division of Mathematics and Statistics, The University of Texas at San Antonio, San Antonio, Texas 78249
Email: ahmad@sphere.math.utsa.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05083-2
Keywords: Positive, component, system, extinction, exponentially
Received by editor(s): December 15, 1997
Published electronically: April 23, 1999
Additional Notes: The author wishes to acknowledge support from SISSA, Trieste, Italy, where this research was completed.
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society

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