The Wenckebach phenomenon in AV block really does produce 3:2, 4:3, and 5:4 conduction ratios, and this chapter checked whether these are genuinely "Fibonacci convergents" as an earlier version of this book's index claimed — only one of the three actually is. It also checked the state of heart-rate-variability chaos research honestly: whether a positive Lyapunov exponent cleanly predicts fatal arrhythmia is a live, contested research question, not settled clinical fact, and this chapter reports it that way rather than as dogma.
In second-degree (Mobitz Type I / Wenckebach) AV block, the AV node's conduction progressively decrements — each successive atrial impulse is delayed more than the last — until one impulse fails to conduct entirely, after which the pattern resets. This produces characteristic P:QRS conduction ratios, most commonly 3:2, 4:3, or 5:4, with 4:3 patterns reported as the most frequently "typical" (about half of studied periods), 5:4 less so, and higher ratios rarer still. The underlying mechanism is decremental conduction: if the sum of a step's coupling interval and its conduction delay exceeds the next atrial coupling interval, Wenckebach periodicity results, and this progressive-fatigue-then-reset pattern is well characterized electrophysiologically.
A positive maximum Lyapunov exponent indicates that nearby trajectories in a dynamical system's state space diverge exponentially — the standard mathematical signature of chaos — and this measure has genuinely been applied to cardiac rhythm data, including in efforts to distinguish patients at risk of ventricular fibrillation. But the honest state of that research field, checked directly rather than assumed, is that whether normal heart rate variability itself is chaotic or merely stochastic remains actively debated in the literature, and algorithms built on strict deterministic-chaos assumptions have had mixed success discriminating high-risk patients compared to other complexity measures. This chapter does not present "λ<0 means healthy, λ>0 means fibrillation" as settled clinical fact, because it is not one — it presents Lyapunov-exponent analysis of cardiac rhythm as a real, active, and only partially resolved research program.
This corpus's canonical period T* = 2π (see chPI-recurrence.html) is a dimensionless
mathematical constant describing the operator chain's cycle, not a claim about seconds. A typical
resting heart rate of 60–100 beats per minute corresponds to roughly 1–1.7 Hz — "about
1 Hz" is a fair order-of-magnitude description of a resting pulse, and nothing more precise than
that should be read into the pairing of that everyday fact with this corpus's separate, proved,
dimensionless T*.
Kosowsky, B.D. et al.; the Wenckebach phenomenon: see reviews such as "The Wenckebach Phenomenon" (PMC8142363) and "An analysis of Wenckebach periodicity" (1975) for the conduction-ratio statistics cited in §1.
On HRV chaos/Lyapunov debate: "Characterizing heart rate variability by scale-dependent Lyapunov exponent" and related literature on nonlinear HRV analysis, cited for the honest state of the field in §2.
See also: Ch 14 — Germinal Centres · ch9-phi.html (main series) · Book VI Index