Two-dimensional constrained chaos and industrial revolution cycles

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Significance

Between the 1760s and the 1980s, three industrial revolutions occurred with almost equal intervals. We explain this phenomenon, which is left untouched in the existing literature. Although the standard theory of discrete-time chaos provides a perfect tool to explain business cycles in a single macroeconomic variable, it is of little use fully to explain innovation dynamics; innovation dynamics inherently involves two state variables representing monopolistically supplied new products and competitively circulating existing products separately. This study unveils two-dimensional ergodic chaos and develops a model of innovation dynamics with these variables. It demonstrates that if the first mover advantage from new products lasts for about 8 y, an industrial revolution-like phenomenon will occur about every 100 y.

Abstract

Since the 1760s, at least three industrial revolutions have occurred. To explain this phenomenon, we introduce two-dimensional (2D) constrained chaos. Using a model of innovation dynamics, we show that an industrial-revolution-like technology burst, driven by investment/saving motives for R&D activities, recurs about every one hundred years if the monopolistic use of a new technology lasts about 8 y.

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Author and article information

Contributors

Makoto Yano:

ORCID: https://orcid.org/0000-0002-2702-1894

Journal

Journal ID (nlm-ta): Proc Natl Acad Sci U S A

Journal ID (iso-abbrev): Proc Natl Acad Sci U S A

Journal ID (publisher-id): PNAS

Title: Proceedings of the National Academy of Sciences of the United States of America

Publisher: National Academy of Sciences

ISSN (Print): 0027-8424

ISSN (Electronic): 1091-6490

Publication date (Electronic, pub): 27 January 2023

Publication date (Print, pub): 31 January 2023

Publication date PMC-release: 27 January 2023

Volume: 120

Issue: 5

Electronic Location Identifier: e2117497120

Affiliations

[1] ^aKyoto University , 606-8501 Kyoto, Japan

[2] ^bResearch Institute of Economy, Trade and Industry , 100-8901 Tokyo, Japan

[3] ^cChuo University , 192-0351 Tokyo, Japan

Author notes

¹To whom correspondence may be addressed. Email: yano@ 123456kier.kyoto-u.ac.jp .

Edited by Jose Scheinkman, Columbia University, New York, NY; received June 5, 2022; accepted December 6, 2022

Author information

Makoto Yano https://orcid.org/0000-0002-2702-1894

Yuichi Furukawa https://orcid.org/0000-0002-6339-5535

Article

Publisher ID: 202117497

DOI: 10.1073/pnas.2117497120

PMC ID: 9945953

PubMed ID: 36706220

SO-VID: cb5a8ac5-d578-4b19-a396-a322eeb70249

License:

This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

History

Date received : 05 June 2022

Date accepted : 06 December 2022

Page count

Pages: 10, Words: 5109