An equivalence theorem concerning population growth in a variable environment

Autor: Ray Redheffer, Richard R. Vance
Jazyk: angličtina
Rok vydání: 2003
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 2003, Iss 43, Pp 2747-2758 (2003)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
01611712
DOI: 10.1155/S0161171203209133
Popis: 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.
Databáze: Directory of Open Access Journals
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