  Bifurcation analysis is used to study an effective model of QCD$_4$ with
four-fermi interactions. Our analysis supports the scenario of a fixed point
merger at the lower edge of the conformal window. This indicates square root
scaling of the anomalous scaling dimensions of the fermion fields just above
the lower edge and exponential scaling just below. We also predict existence of
new fixed points in this model whose (dis)appearance may indicate transitions
of the flow within the conformal window. Furthermore, we make new predictions
for the critical value $(N_{f}/N_{c})_{\textrm{crit}}$ at the lower edge. We
also obtain exotic spiraling flows that are generated by complex scaling
dimensions of the effective four-fermi interactions. Finally, we extend the
model by adding a scalar field that couples with a Yukawa interaction term and
study the modifications it causes to RG-flows.

High Energy Physics - Theory