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Structural Chaos

Published online by Cambridge University Press:  01 January 2022

Conor Mayo-Wilson
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Abstract

A dynamical system is called chaotic if small changes to its initial conditions can create large changes in its behavior. By analogy, we call a dynamical system structurally chaotic if small changes to the equations describing the evolution of the system produce large changes in its behavior. Although there are many definitions of “chaos,” there are few mathematically precise candidate definitions of “structural chaos.” I propose a definition, and I explain two new theorems that show that a set of models is structurally chaotic if it contains a chaotic function. I conclude by discussing the relationship between structural chaos and structural stability.

Type
Classical Physics
Information
Philosophy of Science , Volume 82 , Issue 5 , December 2015 , pp. 1236 - 1247
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

Thanks to Seamus Bradley, Roman Frigg, and Charlotte Werndl for extensive comments on earlier drafts of this article. I am also indebted to conference participants at Mathematizing Science (at the University of East Anglia), the British Society for Philosophy of Science, and the Philosophy of Science Association for suggestions about how to improve this article. Finally, thanks to an anonymous referee, who suggested extending the discussion of structural stability.

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