All of cbwallace2013@icloud.com's Comments + Replies
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.
13moThat would be great.
The list of fields you gave makes me a little nervous, so I should clarify that
I'm looking for specific, practical applications that have become widespread and
paid off. ApEn is better than nothing, but was outcompeted in every application.
Most of the applications of chaos to ecology were retroactive explanations, with
an occasional prediction, but almost never a story like "we implemented
chaos-derived management in these fisheries and they did better/worse than
control fisheries".
The sheer volume of applications that never went anywhere makes it hard to find
the successful practical applications, so I'm very grateful for pointers. But I
do need pointers to specific successes, not fields where the math was tried.
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, O... (read more)