Circadian Clock

Goodwin oscillator — 24-hour gene expression cycle with light entrainment
Goodwin Oscillator
dx/dt = v₁/(1+(z/K)ⁿ) − d₁x
dy/dt = v₂x − d₂y
dz/dt = v₃y − d₃z

x = mRNA (CLOCK/BMAL1)
y = Protein (PER/CRY)
z = Nuclear repressor

Light input resets the phase.