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 can convert an attractor from chaotic to nonchaotic or vice versa. We call a parameter value where this can happen uncertain. The probability that a random choice of the parameter is uncertain commonly scales like a power law in . 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.
- Received 24 June 2014
DOI:https://doi.org/10.1103/PhysRevLett.113.084101
© 2014 American Physical Society