How certain can we be that an attractor is chaotic: Universal
parameter scaling of chaos versus periodicity.
Edward Ott, University of Maryland, USA
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 non-chaotic 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.