Chaos Lab

Continuous flow · dim 3

Van der Pol oscillator

Nonlinear relaxation oscillator. The unforced equation gives a stable limit cycle; the forced version exhibits chaos and devil's staircase frequency locking.

Forced Van der Pol oscillator.

Equations

d²x/dt² − μ (1 − x²) dx/dt + x = A cos(ω t)

At a glance

Parametersμ, A, ω
Chaotic forforced regime, large μ, suitable A and ω
HistoryVan der Pol (1920s); chaos in the forced version studied since the 1970s.

Try it

Open the interactive playground at /tools/vanderpol.

See also

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