Heart and Lung as a Relaxation Oscillator

Heart and lung are the same FitzHugh–Nagumo relaxation oscillator built on the R19 cubic switch. Only the slow recovery time τ_s differs — 18 for the heart, 95 for the lung — so one mechanism produces a fast cardiac beat and a slow respiratory cycle. Both run as sustained limit cycles; the mechanism is grade [V].

One FitzHugh–Nagumo unit, ds/dt = (E(γs−s³)−Iw+drive)/τ_f, serves both organs; only τ_s (18 heart, 95 lung) sets the rhythm. Larger τ_s → slower cycle. [V].

The shared relaxation oscillator

Both pacemakers are one FitzHugh–Nagumo unit: a fast excitable variable s with cubic nonlinearity and a slow recovery variable w, ds/dt = (E(γs − s³) − I w + drive)/τ_f, dw/dt = (s − βw)/τ_s. The cubic is the same R19 bistable form used everywhere in this program; nothing organ-specific is added beyond γ and τ_s.

The slow recovery time sets the rhythm: larger τ_s means a slower relaxation cycle. The heart uses τ_s = 18 and the lung τ_s = 95, which is precisely why one mechanism yields a fast cardiac beat and a slow respiratory cycle.

Both organs oscillate

Run free, each unit produces a sustained limit cycle rather than a fixed point. Over a fixed window the heart completes 115 cycles and the lung 28, the expected fast/slow split.

Grade

The oscillator mechanism is verified [V] from the shared substrate; the absolute rate is set by the cited anchor, not emergent, and is treated separately in the next section.