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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A nonautonomous 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 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