Van der Pol Oscillator


	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.


	Contributed by: Adriano Pascoletti

The van der Pol oscillator is governed by the equations

and

This same equation could also model the displacement

and the velocity

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

(last Snapshot) the system is a harmonic oscillator.

van der Pol Equation (Wolfram MathWorld)

"Van der Pol Oscillator" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/VanDerPolOscillator/

Contributed by: Adriano Pascoletti

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