Brane-bulk energy exchange : a model with the present universe as a   global attractor
  The role of brane-bulk energy exchange and of an induced gravity term on a single braneworld of negative tension and vanishing effective cosmological constant is studied. It is shown that for the physically interesting cases of dust and radiation a unique global attractor which can realize our present universe (accelerating and 0<Omega_{m0}<1) exists for a wide range of the parameters of the model. For Omega_{m0}=0.3, independently of the other parameters, the model predicts that the equation of state for the dark energy today is w_{DE,0}=-1.4, while Omega_{m0}=0.03 leads to w_{DE,0}=-1.03. In addition, during its evolution, w_{DE} crosses the w_{DE}=-1 line to smaller values. 
G. Kofinas, G. Panotopoulos, T.N. Tomaras