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.