Cepheid Pulsation Oscillator & Phase Lag (2D)

A 2D companion to the 3D Cepheid pulsation simulator, built on an independent mechanism: instead of prescribing radius and temperature as fixed sine and cosine curves, this model numerically integrates a self-excited Van der Pol-type oscillator — the same "negative damping" mathematics used to represent the κ-mechanism's opacity valve — and lets the pulsation emerge on its own from that nonlinear equation. The natural frequency still comes from the real period–mean-density relation, but the actual simulated period can drift a few percent from that theoretical value as the drive strength μ grows, just as real relaxation oscillators do. Surface temperature is derived from a genuine first-order thermal-lag filter responding to adiabatic compression, so its phase delay behind radius is a measured, emergent quantity you can compare live against the filter's analytic prediction, rather than a hand-picked quarter cycle. Luminosity still closes the loop through the unavoidable Stefan–Boltzmann law. A phase-space portrait (velocity vs. displacement) shows the pulsation as a closed limit-cycle loop — a view no rotating 3D camera angle can offer directly.