A Primer on Logistic Growth and Substitution
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TL;DR
The mathematics underlying the Loglet Lab software package for loglet analysis describes the decomposition of growth and diusion into S-shaped logistic components, roughly analogous to wavelet analysis, popular for signal processing and compression.
Abstract
This article describes the mathematics underlying the Loglet Lab software package for loglet analysis. “Loglet analysis” refers to the decomposition of growth and diffusion into S-shaped logistic components, roughly analogous to wavelet analysis, popular for signal processing and compression. The term “loglet” joins “logistic” and “wavelet.” Loglet analysis comprises two models: the first is the component logistic model, in which autonomous systems exhibit logistic growth. The second is the logistic substitution model, which models the effects of competitions within a market. An appendix describes the current status of the software.
