This circuit is a external synchronous self oscillator ZVS converter.
As long as voltage at point Vg1 don't go below V1 * R5/(R5+R8) = 2.44V the MOSFET will be OFF. So we can force this by switching ON the BJT or circuit can do it
"himself" via D3 or D2 if the BJT is OFF.
Can you suggest me, how to replace the BJT with a AND gate.