  We extend a generic class of systems which have previously been shown to
spontaneously develop scaling (power law) distributions of their elementary
degrees of freedom.
  While the previous systems were linear and exploded exponentially for certain
parameter ranges, the new systems fulfill nonlinear time evolution equations
similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics
and evolve spontaneously towards "fixed trajectories" indexed by the average
value of their degrees of freedom (which corresponds to the SSB order
parameter). The "fixed trajectories" dynamics evolves on the edge between
explosion and collapse/extinction.
  The systems present power laws with exponents which in a wide range ($\alpha
< -2.$) are universally determined by the ratio between the minimal and the
average values of the degrees of freedom. The time fluctuations are governed by
Levy distributions of corresponding power. For exponents $\alpha > -2$ there is
no "thermodynamic limit" and the fluctuations are dominated by a few, largest
degrees of freedom which leads to macroscopic fluctuations, chaos and
bursts/intermitency.
