  We study the multiple solutions of the truncated propagator Dyson-Schwinger
equation for a simple fermion theory with Yukawa coupling to a scalar field.
Upon increasing the coupling constant $g$, other parameters being fixed, more
than one non-perturbative solution breaking chiral symmetry becomes possible
and we find these numerically. These ``recurrences'' appear as a mechanism to
generate different fermion generations as quanta of the same fundamental field
in an interacting field theory, without assuming any composite structure. The
number of recurrences or flavors is reduced to a question about the value of
the Yukawa coupling, and has no special profound significance in the Standard
Model. The resulting mass function can have one or more nodes and the
measurement that potentially detects them can be thought of as a collider-based
test of the virtual dispersion relation $E=\sqrt{p^2+M(p^2)^2}$ for the charged
lepton member of each family. This requires three independent measurements of
the charged lepton's energy, three-momentum and off-shellness. We illustrate
how this can be achieved for the (more difficult) case of the tau lepton.
