Van der Pol Oscillator — Limit Cycle

The Van der Pol equation ẍ − μ(1−x²)ẋ + x = 0 has a unique stable limit cycle for all μ > 0. The nonlinear damping term pumps energy in for |x| < 1 and dissipates it for |x| > 1, trapping every trajectory onto the same closed orbit by the Poincaré-Bendixson theorem.

μ (damping)1.00
Trajectories5
Speed3
Phase portrait: x vs ẋ | Time series on right