WOLFRAM NOTEBOOK

Van der Pol Oscillator

​
time t
10
parameter μ
0.75
The van der Pol equations emerge in the study of a closed loop electrical circuit consisting of an inductor, a capacitor, and a nonlinear resistor. It is a classical example of a nonconservative nonlinear system with a stable limit cycle.

Details

The van der Pol oscillator is governed by the equations
′
x
(t)=v(t)
and
′
v
(t)=μv(t)1-
2
x(t)
-x(t)
.
This same equation could also model the displacement
x
and the velocity
v
of a mass-spring system with a strange frictional force dissipating energy for large velocities and feeding energy for small ones. This behavior gives rise to self-sustained oscillations (a stable limit cycle). At
μ0
(last Snapshot) the system is a harmonic oscillator.

External Links

Permanent Citation

Adriano Pascoletti
​
​"Van der Pol Oscillator"​
​http://demonstrations.wolfram.com/VanDerPolOscillator/​
​Wolfram Demonstrations Project​
​Published: September 27, 2007
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