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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 ofdoi:10.1088/1126-6708/2006/01/107 fatcat:gnj3g2lk4fbvtd6cvp3u67ukce