Tendency to bifurcate can often be utilized to improve performance characteristics of amplifiers or even to build detectors. Bloch oscillating transistor is such a device. Here we show that bistable behaviour can be approached by tuning the base current and that the critical value depends on the Josephson coupling energy $E_J$ of the device. We demonstrate record-large current gains for device operation near the bifurcation point at small $E_J$. From our results for the current gains at various $E_J$, we determine the bifurcation threshold on the $E_J$ - base current plane. The bifurcation threshold curve can be understood using the interplay of inter- and intra-band tunneling events.
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