Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: April 23, 1999
MathSciNet review: 1636914
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34C35, 34D05

Retrieve articles in all journals with MSC (1991): 34C35, 34D05


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: http://dx.doi.org/10.1090/S0002-9939-99-05083-2
PII: S 0002-9939(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