Duffing Resonator — Phase Portrait & Poincaré Map (2D)

Nanoresonators — the vibrating cores of NEMS oscillators, mass sensors and gyroscopes — behave like a textbook damped spring only while their vibration amplitude stays small; push a doubly-clamped nanobeam harder and its cubic (Duffing) restoring force takes over. This 2D companion simulator integrates the identical driven-damped Duffing equation with an independent RK4 solver, but reads it out the way a physicist actually diagnoses a nonlinear resonator: a phase-space (x, v) trajectory that spirals onto its steady orbit, a Poincaré map built by strobing that trajectory once per drive cycle, and a scrolling time-domain waveform. Sweep the drive frequency slowly through resonance and watch the phase-portrait loop and its Poincaré point snap between two distinct stable orbits — the same bistable jump and hysteresis measured on real NEMS/MEMS devices in the lab, seen here from the dynamical-systems side instead of the mechanical one.