Hystereses and catastrophes were experimentally investigated in a cavity-based scramjet combustor. The inflow Mach number was 3.0. Fuel Equivalence Ratio (ER) was continuously regulated with multi-steps to explore influences of historical regulation directions on combustion states. Two divided hysteresis loops with catastrophes were observed. By 1-D flow estimations, the first loop occurred with shock-free/separated scramjet mode transitions, while the second kept in the separated scramjet mode. This breaks through the traditional knowledge that hysteresis and catastrophe were certainly related to ramjet/scramjet mode transitions. The first hysteresis and catastrophes were attributed to flame stabilization mode transitions between the cavity shear-layer stabilized and the jet-wake stabilized, with flow separation establishment/vanishment upstream the cavities. The obvious variations of flame and shock/separation structures meant large wall-pressure changes in the expansive duct, and generated obvious thrust catastrophes. Besides, transition ER and catastrophe were larger in historical ER-increasing path because combustion efficiency became obviously larger as flow separation established. Difference of critical transition ERs meant the first hysteresis. The second hysteresis and catastrophes in the jet-wake stabilized mode were attributed to flame/shock interaction mode transitions between the flame/shock weak interaction mode and intensive interaction mode. Each transition caused slightly stronger/weaker flame interacting with slightly larger/smaller flow separation, which meant small wall-pressure changes in the expansive duct, and thus thrust catastrophe was unobvious. Hysteresis occurred as the critical transition ER was slightly higher in historical ER-increasing path because of slightly lower combustion efficiency under slightly smaller separation.