On the Classification Scheme for Phenomenological Universalities in Growth Problems in Physics and Other Sciences

TL;DR

This paper critiques a previous classification scheme for growth models, demonstrating its inaccuracies, especially for biological and social systems, and introduces an extended model that derives the involuted Gompertz growth function.

Contribution

It identifies flaws in the existing scheme and proposes an extended model that accurately captures involuted growth behaviors.

Findings

The original West-like growth function is incorrect.

The approach neglects atrophic and involutive growth.

An extended model deriving the involuted Gompertz function is proposed.

Abstract

Comment on "Classification Scheme for Phenomenological Universalities in Growth Problems in Physics and Other Sciences" by P. Castorina, P. P. Delsanto and C. Guiot, Phys. Rev. Lett. {\bf 96}, 188701 (2006) is presented. It has been proved that the West-like function of growth derived by the authors is incorrect and the approach does not take into account the growth of the biological systems undergoing atrophy or demographic and economic systems undergoing involution or regression. A simple extension of the model, which permits derivation of the so far unknown involuted Gompertz function of growth is proposed.