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.
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.
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