We analyze the hybrid absorptive-dispersive optical bistability (OB) behavior in an open -type three-level atomic system by using a microwave field to drive the hyperfine transition between two lower states, along with the consideration of incoherent pumping and spontaneously generated coherence. Different from the closed system, we show that the bistable threshold intensity and related hysteresis loop can be controlled by adjusting the ratio between atomic injection and exit rates. More interestingly, the appearance and disappearance of OB can be transformed mutually by varying the relative phase of three coherent fields under the condition of a strong spontaneously generated coherence. The manipulation of OB behavior through the intensity of the microwave field and the atomic cooperation parameter is also analyzed.
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