1-DOF Duffing sweep

The frequency-sweep quickstart is the canonical runnable 1-DOF Duffing example. This page highlights the modelling and analysis choices that become important in a real study.

The scalar cubic coefficient b[0, 0, 0, 0] controls hardening when positive and softening when negative. Sweep in the resonance region, retain enough periods to resolve the desired harmonics, and increase n_init_cond if jumps or coexisting attractors are plausible.

b = jnp.array([[[[0.2]]]])
oscillator = poscidyn.NonlinearOscillator(
    omega_0=jnp.array([1.0]), Q=jnp.array([80.0]),
    a=jnp.zeros((1, 1, 1)), b=b,
)

When comparing forward and backward curves, first check result.stats["success_rate"]. Then repeat a smaller frequency interval with more initial conditions to determine whether a feature survives the multistart sampling. A selected synthetic curve is evidence to investigate, not by itself a complete bifurcation analysis.