dx/dt = βx(t-τ)/(1+x(t-τ)ⁿ) − γx(t). A single delay τ drives bifurcation from steady state → limit cycle → quasi-periodic → chaos. Originally proposed for blood cell production (Mackey & Glass, 1977). Prototype for physiological time-delay chaos.
τ < 4.5: stable fixed point. τ ~ 7: Hopf bifurcation → limit cycle. τ ~ 13: period doubling. τ > 16.8: chaos (Lyapunov exponent > 0). Mackey-Glass became the canonical test bed for nonlinear time series analysis and embedding theorems (Takens 1981).