Bistability can be between equilibria and equilibria or between equilibria and periodic solutions. If the same system is stimulated with an applied transmembrane current, current pulses can knock the system from one stable state to the other. The following MPEG file illustrates this. This reflects the excitability of the system. This is the idea behind adaptation.
Adaptation is difficult to define precisely.
Some people define adaptation as the return to an initial state when the stimulus is stepped up to a constant value. The constant stimulus initiates oscillations whose frequency decreases slowly and then disappear altogether. The model mimics the membrane potential of an individual pancreatic beta cell at subthreshold glucose levels with an applied current stimulus. If a system is bistable a slow change in the stimulus can cause transitions between stable equilibria and periodic solutions. A slowly changing regulatory chemical or process can do pretty much the same thing.