On the Gompertzian dynamics of growth and self-organization

TL;DR

This paper critiques Waliszewski's application of a Schrödinger-like equation with Morse potential to Gompertzian growth, clarifying prior work and identifying errors in the original model.

Contribution

It clarifies that the core idea was previously introduced and highlights mathematical inconsistencies in Waliszewski's model.

Findings

The main idea predates Waliszewski's work by two years.

Identified mathematical errors in the existing model.

Reaffirmed the earlier formulation of Gompertzian dynamics.

Abstract

Comment on the Waliszewski's article "A principle of fractal-sto-chastic dualism and Gompertzian dynamics of growth and self-organization" (BioSystems 82 (2005)61-73) is presented. It has been proved that the main idea of this work that Gompertzian dynamics is governed by the Schr\"{o}dinger-like equation including anharmonic Morse potential has been already introduced by Molski and Konarski in 2003. Some inconsistencies and mathematical errors in the Waliszewski's model are also pointed out.