Analytical modelling of terminal properties in industrial growth

TL;DR

This paper uses nonlinear dynamics and analytical models to explore the terminal behavior of industrial growth, emphasizing the inevitability of saturation over time, supported by empirical data from IBM.

Contribution

It introduces simple analytical models from nonlinear dynamics to understand long-term saturation in industrial growth, integrating the Balanced Scorecard concept.

Findings

Growth can be exponential in short term but saturates long term.

Mathematical models predict saturation under various conditions.

Empirical data from IBM supports the models.

Abstract

In this pedagogical study, carried out by adopting standard mathematical methods of nonlinear dynamics, we have presented some simple analytical models to understand terminal behaviour in industrial growth. This issue has also been addressed from a dynamical systems perspective, with especial emphasis on the concept of the Balanced Scorecard. Our study enables us to make the general claim that although the fortunes of an industrial organization can rise with exponential rapidity on relatively short time scales, its growth will ultimately and inevitably be saturated on long time scales by various factors which are nonlinear in character. We have mathematically demonstrated the likely occurrence of this feature under various possible circumstances, including the Red Ocean and the Blue Ocean. Finally and most importantly, our arguments and their associated mathematical modelling have received remarkable support from the growth pattern indicated by empirical data gathered from a well-recognized global company like IBM.