The logistic population model with slowly varying carrying capacity

Shepherd, J and Stojkov, L 2007, 'The logistic population model with slowly varying carrying capacity', Australian and New Zealand Industrial and Applied Mathematics Journal , vol. 47, pp. 492-506.


Document type: Journal Article
Collection: Journal Articles

Title The logistic population model with slowly varying carrying capacity
Author(s) Shepherd, J
Stojkov, L
Year 2007
Journal name Australian and New Zealand Industrial and Applied Mathematics Journal
Volume number 47
Start page 492
End page 506
Total pages 14
Publisher Australian Mathematical Society
Abstract Many single-species differential equation population models feature a carrying capacity---the limiting population supportable by the environment. For constant carrying capacities an exact solution may often be found, representing the evolving population in time. However, for time varying carrying capacities, exact solution is rarely possible, and numerical techniques must be used. We demonstrate that when the carrying capacity varies slowly with time, a multiple time scale analysis leads to approximate closed form solutions that, apart from being explicit, are comparable to numerically generated ones and which are valid for a range of parameter values.
Subject Approximation Theory and Asymptotic Methods
Copyright notice © Austral. Mathematical Soc. 2007.
ISSN 1446-8735
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