  Nonlinear dynamical systems, ranging from insect populations to lasers and
chemical reactions, might exhibit sensitivity to small perturbations in their
control parameters, resulting in uncertainties on the predictability of tunning
parameters that lead these systems to either a chaotic or a periodic behavior.
By quantifying such uncertainties in four different classes of nonlinear
systems, we show that this sensitivity is to be expected because the boundary
between the sets of parameters leading to chaos and to periodicity is fractal.
Moreover, the dimension of this fractal boundary was shown to be roughly the
same for these classes of systems. Using an heuristic model for the way
periodic windows appear in parameter spaces, we provide an explanation for the
universal character of this fractal boundary.
