<p>We study the cosmological dynamics of non-minimally coupled matter models using Brown’s variational approach to relativistic fluids in General Relativity. After decomposing the Ricci scalar into a bulk and a boundary term, we construct new models by coupling the bulk term to the fluid variables and an external scalar field. Using dynamical systems techniques, we study models of this type and find that they can give rise to both early-time inflationary behaviour and late-time accelerated expansion. Moreover, these models also contain very interesting features that are rarely seen in this context. For example, we find dark energy models which exhibit phantom crossing in the recent past. Other possibilities include models that give a viable past evolution but terminate in a matter-dominated universe. The dynamical systems themselves display an array of mathematically interesting phenomena, including spirals, centres, and non-trivial bifurcations depending on the chosen parameter values.</p>