  A cosmological model with van der Waals gas and dust has been studied in the
context of a three-component autonomous non-linear dynamical system involving
the time evolution of the particle number density, the Hubble parameter and the
temperature. Due to the presence of a symmetry of the model, the temperature
evolution law is determined (in terms of the particle number density) and with
this the dynamical system reduces to a two-component one which is fully
integrable. The globally conserved Hamiltonian is identified and, in addition
to it, some special (second) integrals, defined and conserved on a
lower-dimensional manifold, are found. The parameter choices and their
implication for the global dynamics in terms of cosmological relevance are
comprehensively studied and the physically meaningful parameter values are
identified.
