Cheyne-Stokes Period and Circulatory Delay
Cheyne–Stokes respiration is the chemoreflex limit cycle in the delay-dominated heart-failure regime, and its period scales as about twice the circulatory transport delay — the model returns a period-versus-delay slope of 1.99, i.e. TCSR ≈ 2×τcirc. A slower circulation lengthens the cycle. Grade [V].
In the fast-plant regime the chemoreflex cycle obeys TCSR ≈ 2 × τcirc; the measured period/delay slope is 1.992 across delays 8–20 s (band [1.7,2.4]). [V].
The forced number: period ≈ twice the delay
Cheyne–Stokes respiration is the chemoreflex limit cycle in the fast-plant, delay-dominated regime typical of heart failure. In that regime the cycle period is set by the loop transport delay, and the model returns a period-versus-delay slope of 1.992 — essentially TCSR ≈ 2 × τcirc.
This factor of two is the forced relation of the page: a delayed negative feedback oscillates with a period of about twice its loop delay. It is recovered across a range of circulatory delays, not at a single point.
| circulatory delay (s) | CSR period (s) | period / delay |
|---|---|---|
| 8 | 17.74 | 2.22 |
| 12 | 25.74 | 2.15 |
| 15 | 31.74 | 2.12 |
| 20 | 41.74 | 2.09 |
Why heart failure lengthens the cycle
Because the period scales with the transport delay, a slower circulation (a longer lung-to-chemoreceptor delay, as in low cardiac output) lengthens the Cheyne–Stokes cycle. The mechanism predicts the clinical direction directly.
Grade
The limit-cycle period scaling as about twice the delay is verified [V] across the delay sweep; the slope lands at 1.992, within the acceptance band [1.7, 2.4].