How to model Tape Saturation (Audio DSP)?
Saturation can be modeled to first order as a symmetrical distortion of the signal, but it also has history dependence--hence the term hysteresis in describing magnetic response to a field that is applied.  Bias (an AC field applied to the tape at the same time as the signal to be recorded) linearizes the curve and reduces hysteresis effects by eradicating the memory of the medium.  If your objective is to simulate the sound of a tape recorder, you should consider hysteresis effects, and the fact that high frequency signals are self-biasing, so that they effectively saturate at a different (lower) level than low-frequency ones.  (This was the insight behind Dolby HX processing, which really made cassette tapes sound a lot better.)