Current universe (assumed here to be normal matter on the brane) is pressureless from observations. In this case the energy condition is $rho_0geq0$ and $p_0=0$. By using this condition, brane models can be distinguished. Then, assuming arbitrary com
ponent of matter in DGP model, we use four known energy conditions to study the matter on the brane. If there is nonnormal matter or energy (for example dark energy with $w<-1/3$) on the brane, the universe is accelerated.
An exact solution of brane universe is studied and the result indicates that Friedmann equations on the brane are modified with an extra term. This term can play the role of dark energy and make the universe accelerate. In order to derive the $Lambda
$CDM Universe from this global brane model, the new solutions are obtained to describe the $5D$ manifold.
We investigate the phantom field with potential $V(phi)=V_{0}exp(-lambda{phi}^2)$ and dark matter in the spatially flat FRW model. It has been shown by numerical calculation that there is a attractor solution in this model. We also apply the statefin
der diagnostic to this phantom model. It is shown that the evolving trajectories of this scenario in the $s-r$ diagram is quite different form other dark energy models.
We study the statefinder parameter in the five-dimensional big bounce model, and apply it to differentiate the attractor solutions of quintessence and phantom field. It is found that the evolving trajectories of these two attractor solutions in the s
tatefinder parameters plane are quite different, and that are different from the statefinder trajectories of other dark energy models.
