Optical bistability via quantum interference from incoherent pumping and spontaneous emission

► We modulate the optical bistability (OB) in a four-level N-type atomic system. ► The threshold of optical bistability can be controlled by the quantum interferences. ► OB converts to optical multi-stability (OM) by the quantum interferences. ► We discuss the effect of an incoherent pumping field on reduction of OB threshold.