On a mathematical model for a damped and driven double-well Bose–Einstein condensate

In this paper we consider a two-mode dynamical system as a model for a driven one-dimensional damped Bose–Einstein condensate in a double-well trapping potential. In the case of a constant external driving force the existence and stability of stationary solutions are discussed in relation to the values of the physical parameters. In the case of a time-dependent periodic external driving force the existence of limit cycles is proved, and the amplitude of these limit cycles exhibits a jump phenomenon for critical values of the physical parameters.