  The tunnelling quantum dynamics of bimodal BJJ system is modified through
introducing an equilibrium condition, which is based on the assumption that the
BJJ is tend to keep on its ground state (with a lowest energy) during the
oscillation. The tunnelling dynamics of BJJ with symmetric and asymmetric traps
is discussed through numerically solving the modified equations. Stationary
states are found to exist in the both BJJs. Compared to previous works, the
macroscopic quantum self trapping (MQST) is auto-avoided. Meanwhile, it is
revealed that the BJJ oscillates with its inherent frequency which is only
related to the Josephson energy, which has been testified experimentally in
other contexts.
