  We study dynamics of non-minimally coupled scalar field cosmological models
with Higgs-like potentials and a negative cosmological constant. In these
models the inflationary stage of the Universe evolution changes into a
quasi-cyclic stage of the Universe evolution with oscillation behaviour of the
Hubble parameter from positive to negative values. Depending on the initial
conditions the Hubble parameter can perform either one or several cycles before
to become negative forever.
