If the observable universe is a braneworld of Randall–Sundrum type, then particle interactions at high energies will produce five-dimensional gravitons that escape into the bulk. As a result, the Weyl energy density on the brane does not behave like radiation in the early universe, but does so only later, in the low-energy regime. Recently a simple model was proposed to describe this modification of the Randall–Sundrum cosmology. We investigate the dynamics of this model, and find the exact solution of the field equations. We use a dynamical systems approach to analyse global features of the phase space of solutions.