<p>One of the current theories about the formation of a planetary system conjectures that traveling waves within a primordial interstellar gas cloud might have led, eventually, to the formation of the planets. As an initial step in this process embedded solid particles within a traveling wave may commence self-gravitational accumulation at the wave crests, where the pressure and density are highest, so possibly leading to the formation of cometary nuclei. To test the validity of this conjecture we present in this paper a prototype model for the evolution of systems of self gravitating particles. This model is applied to linear and circular traveling waves and ensembles of particles in a disk. We show that under proper conditions these systems might undergo a bifurcation or “self organization” which leads to the formation of cometary nuclei.</p>