  In this study, we present the phase-space analysis of Quintessence models
specified by the choice of two potentials, namely the Recliner potential and
what we call the broken exponential-law potential, which is a new proposal.
Using a dynamical system analysis we provide a systematic study of the
cosmological evolution of the two models and their properties. We find new
scaling solutions characterised by a constant ratio between the energy density
of the scalar field and that of the matter component. These solutions are of
high interest in light of the possibility to alleviate the coincidence problem.
Additionally, the models also show attractor solutions. We finally construct
concrete models built using a double potential according to which one potential
realises the early-time scaling regime and the second one allows to exit this
regime and to enter in the epoch of cosmic acceleration driven by a
scalar-field dominated attractor point.
