Cavity-mediated Bose-Einstein condensates (BECs) systems,[1-5] particularly the system of BEC trapped in a double well (DW) coupling to a driven cavity mode,have been theoretically investigated in recent years.[6-8] It is found that the cavity-field alters the locations and the amount of stationary points and causes new motional modes of the Bose-Josephson junction (B J J),and the causation of these phenomena is the nonlinearity of cavity-field-induced tilt.[6]It is also shown that the cavity mode not only interacts with the condensates and modifies their motions,but also carries the population information of the atoms as the intra-cavity-photons leaking out of the cavity.Therefore,the nonlinearity arising from atomcavity field interaction can promote the Josephson oscillation and has an important role in causing the pseudo-self-trapping,self-organization and collapserevival adequately.