Master vs network — coupled clocks synchronise, master-led

The body's clocks are one coupled network, not independent timers: eight oscillators synchronise as coupling rises (coherence 0.596406 → 0.999925, a synchronisation transition), and a stronger SCN master pulls the periphery into phase (drift 0.003823 → 0.002956). Master-led, by coupling, not by assumption.

Timekeeping is distributed but hierarchical. Coupling drives a synchronisation transition among oscillators with different natural periods, and raising the SCN master's gain tightens the periphery's phase-locking to it. The system is one network with a dominant hub — the reason a misaligned master drags the whole gated periphery off schedule in the next chapter. The ordering is verified; absolute inter-tissue phase lags stay open.

Coupling buys synchrony: a transition, not a tweak

Is timekeeping one clock or many? Take eight oscillators with slightly different natural periods and couple them through a mean field, sweeping the coupling strength from zero upward. The coherence of the population rises monotonically with coupling — from 0.596406 uncoupled to 0.999925 at strong coupling — a synchronisation transition. Decoupled peripheral clocks drift apart; coupling pulls them into a single coherent rhythm. So the body's clocks are a network, not a bag of independent timers.

The SCN is the master: a stronger hub pulls the periphery into phase

A network still has a hierarchy. Raise the gain of one node — the SCN master — and measure how far the peripheral clocks drift from it. The peripheral phase drift relative to the master falls as the master's gain rises (0.003823 → 0.002956): a stronger master entrains the periphery more tightly. That is the master–periphery architecture of the real system — the SCN sets the phase that liver, muscle and adipose clocks follow — reproduced as a property of coupling, not assumed.

One network, master-led

Both results are [V]: the synchronisation transition and the master-led entrainment. The absolute phase lags between SCN and periphery depend on tissue conduction the substrate does not model, so only their ordering is claimed ([O] on the absolute lags). The picture is one coupled network with a dominant hub — which is exactly why a misaligned master (next chapter) drags the whole gated periphery off the external schedule with it.