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

John H.M. Thornley, John J. Shepherd and J. France

Ecological Modelling, 2007, vol. 204, issue 3, 531-534

Abstract: 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.

Keywords: Logistic; θ-Logistic; Power-law-logistic; Generalized logistic; Model; Growth; Development; Variable asymptote; Open-ended; Analytical solutions (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecomod:v:204:y:2007:i:3:p:531-534

DOI: 10.1016/j.ecolmodel.2006.12.026

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