  Cosmological models can be studied effectively using dynamical systems
techniques. Starting from Brown's formulation of the variational principle for
relativistic fluids, we introduce new types of couplings involving a perfect
fluid, a scalar field, and boundary terms. We describe three different coupling
models, one of which turns out to be particularly relevant for cosmology. Its
behaviour is similar to that of models in which dark matter decays into dark
energy. In particular, for a constant coupling, the model mimics well-known
dynamical dark energy models while the non-constant couplings offer a rich
dynamical structure, unseen before. We are able to achieve this richness whilst
working in a two-dimensional phase space. This is a significant advantage which
allows us to provide a clear physical interpretation of the key features and
draw analogies with previously studied models.
