International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 127350 | https://doi.org/10.1155/S0161171203209133

Ray Redheffer, Richard R. Vance, "An equivalence theorem concerning population growth in a variable environment", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 127350, 12 pages, 2003. https://doi.org/10.1155/S0161171203209133

An equivalence theorem concerning population growth in a variable environment

Received16 Sep 2002

Abstract

We give conditions under which two solutions x and y of the Kolmogorov equation x˙=xf(t,x) satisfy limy(t)/x(t)=1 as t. This conclusion is important for two reasons: it shows that the long-time behavior of the population is independent of the initial condition and it applies to ecological systems in which the coefficients are time dependent. Our first application is to an equation of Weissing and Huisman for growth and competition in a light gradient. Our second application is to a nonautonomous generalization of the Turner-Bradley-Kirk-Pruitt equation, which even before generalization, includes several problems of ecological interest.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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