Chaos Lab

Continuous flow · dim

Mackey-Glass

1977 model of physiological control (white blood cell production) with delayed feedback. Infinite-dimensional state space due to the delay. Standard benchmark for chaotic time-series prediction and reservoir computing.

Top: scalar time series x(t). Bottom: x(t) vs x(t − τ) delay embedding revealing the attractor.

Equations

dx/dt = β · x(t − τ) / (1 + x(t − τ)^n) − γ · x(t)

At a glance

Parametersβ = 0.2, γ = 0.1, n = 10, τ = 17 (standard benchmark)
Chaotic forτ > 16.8 (standard)
HistoryMackey and Glass, Science (1977).

Try it

Open the interactive playground at /tools/mackey-glass.

See also

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