Complex hysteresis

Hysteresis typically refers to subcritical transitions between two stable attractors at two different values of a control parameter. We address here a different form of hysteresis, referred to as complex hysteresis, where a stable attractor and a chaotic attractor coexist. However, depending on the direction of variation of the control parameter, the chaotic state can be observed or cannot be observed. We address the phenomenon of complex hysteresis in one-dimensional maps as well as in a real flow.