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An open-ended logistic-based growth function: analytical solutions and the power-law logistic model

Thornley, John H. M.; Shepherd, John J.; France, J.. 2007 An open-ended logistic-based growth function: analytical solutions and the power-law logistic model. Ecological Modelling, 204 (3-4). 531-534. 10.1016/j.ecolmodel.2006.12.026

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Abstract/Summary

An open-ended form of the logistic equation was recently proposed, using a model comprising two differential equations [Thornley, J.H.M., France, J., 2005. An open-ended logistic-based growth function. Ecol. Model. 184, 257–261]. The equations represent the two processes of growth and development, and are coupled. In this note, an analytical solution is developed for constant parameters. The solution can be expressed as a targetted single-differential-equation model, the θ-logistic or power-law logistic model, which is a well-known empirical growth equation in ecology and elsewhere. The analysis may facilitate mechanistic interpretation and application of the power-law logistic model as well as the original open two-differential-equation model.

Item Type: Publication - Article
Digital Object Identifier (DOI): 10.1016/j.ecolmodel.2006.12.026
Programmes: CEH Programmes pre-2009 publications > Biodiversity
CEH Sections: CEH fellows
ISSN: 0304-3800
Additional Keywords: Logistic, θ-Logistic, Power-law-logistic, Generalized logistic, Model Growth, Development, Variable asymptote, Open-ended, Analytical solutions
NORA Subject Terms: Ecology and Environment
Mathematics
Date made live: 21 May 2008 09:49
URI: http://nora.nerc.ac.uk/id/eprint/3094

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