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

μ0

(last Snapshot) the system is a harmonic oscillator.

External Links

van der Pol Equation (Wolfram MathWorld)

Permanent Citation

Adriano Pascoletti

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