Optical bistability and multi-stability via voltage-controlled and the rate of incoherent pump in a quantum dot nanostructure

► It is found that the OB can be controlled via tunnel coupling and the incoherent pump. ► It is demonstrated that the voltage-controlled detuning can affect the behavior of OB and OM. ► It is realized the OM converts to OB only by the rate of incoherent pump.