cbwallace2013@icloud.com

Quick look: applications of chaos theory

Elizabeth and Alex - This is an interesting article. More broadly, there is a significant community of scientists/engineers/mathematicians that have worked in dynamical systems, nonlinear dynamics, chaos theory, and applications of chaotic dynamics. A reasonable number of technical monographs and textbooks have been written on these areas since the early to mid 1980’s. Applications exist in electrical engineering, mechanical engineering, fluid dynamics, biology, ecology, economics, networks, medical science, applied mathematics,…. I am not sure whether you want to do a follow up article, or devote time to further investigation, but I am happy to provide pointers to relevant literature if you like.

Here are my initial suggestions, keeping in mind that chaos theory is a subset of dynamical systems theory. For some modern applications it has been subsumed as an element of applied complexity science.

1. The Predictors: How a band of maverick physicists used chaos theory to trade their way to a fortune on Wall Street, Thomas A. Bass, Henry Holt and Company, New York, 1999.

2. Increasing Returns and Path Dependence in the Economy, W. Brian Arthur, The University of Michigan Press, 1994

3. Complexity and the Economy, W. Brian Arthur, Oxford University Press, 2015

4. Complexity Economics, Dialogues of the Applied Complexity Network, W. Brian Arthur, Eric D. Beinhocker, Allison Stanger, Editors, SFI Press, 2020

5. Making Sense of Chaos: A Better Economics for a Better World, J. Doyne Farmer, Penguin Random House UK, 2024

6. Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, 2nd Edition, Robert C. Hilborn, Oxford University Press, 2000. Take a look at Chapter 11 and Chapter 12.

7. Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors, Eckehard Scholl, Cambridge University Press, 2001

8. Chaos in Circuits and Systems, Guanrong Chen and Tetsushi Ueta, Editors, World Scientific Press, 2002. Recommended Chapters: 5, 6,10, 12,13, 17, 22, 23, 24, 26, 27.

Many of the engineering applications can be found in application dependent modern circuit designs. Spread spectrum communications and advanced defense electronic applications make use of tools and methods from items 6, 7, and 8.

I hope these are helpful.