Controlling double-cavity optical switching in a K-type multilevel system including spontaneously generated coherence

► Optical bistability (OB) in a K-type atomic medium inside a double optical cavity. ► Controllability of OB via electromagnetic fields not circulating in the cavities. ► Controllability of OB via spontaneously generated coherence due to decaying levels. ► The system displays a new class of bifurcations.