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

Quick quiz

Test yourself on mackey-glass

8 multiple-choice questions. Pick an answer for each, then submit to see explanations.

  1. Q1.Mackey-Glass models:

  2. Q2.At standard parameters and τ > 16.8, the dynamics are:

  3. Q3.Mackey-Glass is famously used as:

  4. Q4.The phase space of Mackey-Glass is:

  5. Q5.The Hill function in Mackey-Glass:

  6. Q6.Increasing n in Mackey-Glass makes feedback:

  7. Q7.Why is Mackey-Glass a 'physiological' chaos model?

  8. Q8.Reservoir computing benchmark uses Mackey-Glass because:

0 of 8 answered