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.
Equations
d²x/dt² − μ (1 − x²) dx/dt + x = A cos(ω t)At a glance
| Parameters | μ, A, ω |
|---|---|
| Chaotic for | forced regime, large μ, suitable A and ω |
| History | Van der Pol (1920s); chaos in the forced version studied since the 1970s. |
Try it
Open the interactive playground at /tools/vanderpol.
See also
Quick quiz
Test yourself on vanderpol
8 multiple-choice questions. Pick an answer for each, then submit to see explanations.
Q1.The unforced Van der Pol oscillator has:
Q2.The Van der Pol equation reads:
Q3.Balthasar van der Pol introduced this equation in:
Q4.For μ ≫ 1 the unforced Van der Pol exhibits:
Q5.Cartwright & Littlewood studied the forced Van der Pol in:
Q6.Van der Pol oscillators model:
Q7.Routes to chaos in the forced Van der Pol include:
Q8.Bonhoeffer-Van der Pol is a relabelling popular in: