  The suprachiasmatic nucleus (SCN), also known as the circadian master clock,
consists of a large population of oscillator neurons. Together, these neurons
produce a coherent signal that drives the body's circadian rhythms. What
properties of the cell-to-cell communication allow the synchronization of these
neurons, despite a wide range of environmental challenges such as fluctuations
in photoperiods? To answer that question, we present a mean-field description
of globally coupled neurons modeled as Goodwin oscillators with standard
Gaussian noise. Provided that the initial conditions of all neurons are
independent and identically distributed, any finite number of neurons becomes
independent and has the same probability distribution in the mean-field limit,
a phenomenon called propagation of chaos. This probability distribution is a
solution to a Vlasov-Fokker-Planck type equation, which can be obtained from
the stochastic particle model. We study, using the macroscopic description, how
the interaction between external noise and intercellular coupling affects the
dynamics of the collective rhythm, and we provide a numerical description of
the bifurcations resulting from the noise-induced transitions. Our numerical
simulations show a noise-induced rhythm generation at low noise intensities,
while the SCN clock is arrhythmic in the high noise setting. Notably, coupling
induces resonance-like behavior at low noise intensities, and varying coupling
strength can cause period locking and variance dissipation even in the presence
of noise.
