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.

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The van der Pol oscillator is governed by the equations x'(t)=v(t) and v'(t)=μ v(t) (1-((x(t))^2))-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.

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Contributed by: Adriano Pascoletti

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