A dynamic nonlinear model for saturation in industrial growth

TL;DR

This paper introduces a nonlinear logistic model to predict long-term saturation in industrial growth, providing a mathematical framework and empirical validation using IBM data.

Contribution

It develops a general nonlinear logistic equation with an integral solution for modeling industrial saturation, supported by empirical data from IBM.

Findings

Predicted limiting values of revenue and human resources.

Established a time scale for nonlinear saturation onset.

Validated model with IBM data.

Abstract

A general nonlinear logistic equation has been proposed to model long-time saturation in industrial growth. An integral solution of this equation has been derived for any arbitrary degree of nonlinearity. A time scale for the onset of nonlinear saturation in industrial growth can be estimated from an equipartition condition between nonlinearity and purely exponential growth. Precise predictions can be made about the limiting values of the annual revenue and the human resource content that an industrial organisation may attain. These variables have also been modelled to set up an autonomous first-order dynamical system, whose equilibrium condition forms a stable node (an attractor state) in a related phase portrait. The theoretical model has received close support from all relevant data pertaining to the well-known global company, IBM.