The menstrual cycle is the slowest relaxation oscillator (T2)

The menstrual cycle is the slowest relaxation oscillator in the package: a long follicular charge and a fast ovulatory discharge, not a sinusoid. The rise/fall timing asymmetry is 309.6 (a pure sinusoid is exactly 1.0), confirming relaxation dynamics. The ~28-day period is a measured anchor set by the recovery timescale τ_s, not derived from the substrate.

Over the run the slow FHN completes 11 cycles with period 1133.7 (arb). The waveform is strongly asymmetric — a short upstroke (3.65) and a long recovery (1130.0), giving an asymmetry ratio of 309.6. A sinusoid would give exactly 1.0, so the shape is unambiguously that of a relaxation oscillator.

A long charge and a fast discharge

The menstrual cycle is a slow oestradiol rise as the dominant follicle grows, then a fast ovulatory excursion (the LH surge), then a luteal plateau and reset. On the substrate this is the same FHN run at the longest recovery timescale, τ_s=600.

The shape discriminant: rise/fall asymmetry

A relaxation oscillator is time-asymmetric (slow rise, fast excursion); a sinusoid is time-symmetric. Measuring the upstroke-to-recovery timing ratio over one period gives 309.6, which a pure sinusoid would render as exactly 1.0.

The fraction of time spent “high” is deliberately not used as the discriminant, because a slow decay sits high for most of a period yet is still relaxation. The timing asymmetry is the clean, boundary-insensitive test, and the realised value sits far above any reasonable threshold.

The ~28-day period is a measured [L] anchor inherited from the recovery timescale; the relaxation character is the sim-verified [V] claim. The period magnitude is not derived.