[en] A simple, non-linear generalization of the M.S.W. equation is presented and its analytic solution is outlined. The density operator of the system is parameterized by a polarization vector, the orbits of which are shown to be periodic and to lie on a sphere. Their non-trivial flow patterns fall into two topological categories. In one instance, the trajectories are orbits about a pair of centres. In the other, a saddle point and associated separatrices isolate the orbits about three centres. The possibility that this more complex flow of trajectories may, if perturbed, become chaotic is discussed. Finally, the relevance of this work, to neutrino oscillations in the early universe, is examined. 13 refs