Logistic Growth and Substitution: The Mathematics of the Loglet Lab Software Package

Perrin S. Meyer, Jason W. Yung, and Jesse H. Ausubel

Abstract

This paper 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'', coined at The Rockefeller University in 1994 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 to this paper describes the current status of the software.

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