Coupled-mode theory for Bose-Einstein condensates with time dependent atomic scattering length

We study nonlinear tunnelling and localization phenomena in Bose-Einstein condensate in a double-well potential, using a coupled-mode theory. We consider the effects induced by the damping and an atomic scattering length oscillating in time in a double-well potential. The existence of synchronous solutions in a running phase mode and resonances in macroscopic quantum tunnelling for such system are investigated. The switching between macroscopic quantum tunnelling and quantum self-trapped regimes induced by periodic modulations of the scattering length is also studied.