Van der Pol / Duffing

Van der Pol and Duffing oscillators with live parameters, nullclines, and Poincaré section.

About this tool

Van der Pol / Duffing — VdP: ẍ−μ(1−x²)ẋ+x=0 has a stable limit cycle. Duffing: ẍ+δẋ+αx+βx³=γ cos(ωt) shows soft/hard springs and chaos. Yellow curves are VdP nullclines; Duffing strobes a Poincaré section once per drive period.