  The catastrophe theory is applied to a nuclear cluster model and an effective
model for QCD at low energy. The study of quantum phase transitions in the
cluster model was considered in an earlier publication, but restricted to
spherical clusters and on a semi-classical level. In the present contribution,
we include the case of deformed clusters and determine the spectrum numerically
as a function of an interaction parameter, where signatures of a quantum phase
transition can be seen. It is shown that in this more complicated case, with
deformation of the clusters, the catastrophe theory can be applied with some
interesting consequences. A further example of a many-body problem is
considered, namely an effective model of QCD, which is able to describe the low
energy hadron spectrum and, when temperature is introduced, even ratios of
particle-antiparticle productions. The catastrophe theory is able to provide
useful information on the phase transition from a perturbative to a
non-perturbative vacuum. This contributions shows the universal usefulness of
catastrophe theory, while more examples of applications to different fields are
mentioned in the Introduction.
