  Dynamics of brane-world models of dark energy is reviewed. We demonstrate
that simple dark energy brane models can be represented as 2-dimensional
dynamical systems of a Newtonian type. Hence a fictitious particle moving in a
potential well characterizes the model. We investigate the dynamics of the
brane models using methods of dynamical systems. The simple brane-world models
can be successfully unified within a single scheme -- an ensemble of brane dark
energy models. We characterize generic models of this ensemble as well as
exceptional ones using the notion of structural stability (instability). Then
due to the Peixoto theorem we can characterize the class of generic brane
models. We show that global dynamics of the generic brane models of dark energy
is topologically equivalent to the concordance $\Lambda$CDM model. We also
demonstrate that the bouncing models or models in which acceleration of the
universe is only transient phenomenon are non-generic (or exceptional cases) in
the ensemble. We argue that the adequate brane model of dark energy should be a
generic case in the ensemble of FRW dynamical systems on the plane.
