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arXiv · 1408.0311

The Scaling of Chaos vs Periodicity: How Certain is it that an Attractor is Chaotic?

Madhura Joglekar·Edward Ott·James A. Yorke
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Abstract

The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $ε$ can convert an attractor from chaotic to non-chaotic or vice-versa. We call a parameter value where this can happen $ε$-uncertain. The probability that a random choice of the parameter is $ε$-uncertain commonly scales like a power law in $ε$. Surprisingly, two seemingly similar ways of defining this scaling, both of physical interest, yield different numerical values for the scaling exponent. We show why this happens and present a quantitative analysis of this phenomenon.

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Madhura Joglekar, Edward Ott, James A. Yorke. 2014-08-01. The Scaling of Chaos vs Periodicity: How Certain is it that an Attractor is Chaotic?. https://doi.org/10.1103/physrevlett.113.084101

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