Slow variation in the Gompertz model

Grozdanovski, T and Shepherd, J 2007, 'Slow variation in the Gompertz model', Australian and New Zealand Industrial and Applied Mathematics Journal, vol. 47, pp. 541-554.


Document type: Journal Article
Collection: Journal Articles

Title Slow variation in the Gompertz model
Author(s) Grozdanovski, T
Shepherd, J
Year 2007
Journal name Australian and New Zealand Industrial and Applied Mathematics Journal
Volume number 47
Start page 541
End page 554
Total pages 13
Publisher Australian Mathematical Society
Abstract In many differential, single species, population models, the intrinsic model parameters are assumed to be given constants. Typical examples are the "carrying capacity" and "rate constant" arising in the logistic model. Such constant parameters usually allow exact solution of the model equations, to completely describe the evolving population. However, this assumption of constancy is not realistic since such parameters may exhibit a wide range of variation with time. This investigation considers a particularly useful population model---the Gompertz model---in the case where the model parameters vary slowly with time. Multi-timing methods construct an approximate expression for the population that has the advantages of being both explicit and giving results comparable to those obtained from numerical calculations.
Subject Approximation Theory and Asymptotic Methods
Copyright notice © Austral. Mathematical Soc. 2007.
ISSN 1446-8735
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