Oestrogen feedback is a bistable switch with hysteresis (T3)

Oestrogen feedback is a bistable R19 switch. Below threshold the axis sits in negative feedback (low LH); sustained high oestradiol crosses the spinodal and flips discontinuously to positive feedback — the mid-cycle LH surge (up-jump 1.634). The switch shows hysteresis (width 0.779): the up-threshold to trigger the surge exceeds the down-threshold to return. It is the same R19 primitive as malignant transformation.

Sweeping the oestradiol-analogue drive up then down, the settled axis state jumps discontinuously by 1.634 at the surge threshold (0.3873), near the spinodal 0.3849. The up- and down-thresholds differ by 0.779 (hysteresis), the signature of a true bistable switch rather than a graded response.

Negative feedback flips to positive at a threshold

For most of the cycle rising oestradiol suppresses LH (negative feedback). Once oestradiol is high enough for long enough the axis crosses the spinodal and the sign of feedback flips: the mid-cycle LH surge is the system snapping into the positive-feedback basin.

The flip is discontinuous, jumping by 1.634 in settled state at the surge threshold 0.3873 — right at the geometric spinodal 0.3849. A graded (sinusoidal-feedback) model has no such jump.

Hysteresis confirms bistability

Sweeping the drive back down, the axis returns at a lower threshold than it left, so the up- and down-thresholds differ by 0.779. This hysteresis loop is the defining fingerprint of a bistable switch and rules out a single-valued response curve.

This is the same R19 bistable primitive the oncology chapter (§8) uses for malignant transformation: the surge and a cancerous fate-flip are one mechanism, read in two tissues. The switch mechanism is sim-verified [V].