Coupled Duffing systems

The one-degree-of-freedom quickstart is the best place to learn the workflow. For coupled systems, the solver interface does not change: only array shapes and non-zero tensor entries do.

import jax.numpy as jnp
import poscidyn

a = jnp.zeros((2, 2, 2)).at[0, 0, 1].set(2.0).at[1, 0, 0].set(1.0)
b = jnp.zeros((2, 2, 2, 2)).at[0, 0, 0, 0].set(0.2)

oscillator = poscidyn.NonlinearOscillator(
    omega_0=jnp.array([1.0, 2.0]),
    Q=jnp.array([50.0, 50.0]),
    a=a,
    b=b,
)
excitation = poscidyn.DirectHarmonicExcitation(f_d=jnp.array([0.002, 0.0]))
solver = poscidyn.TimeIntegration(
    oscillator=oscillator,
    excitation=excitation,
    response_measure=poscidyn.Demodulation(
        multiples=(1.0,), modal_contributions=jnp.array([1.0, 1.0])
    ),
    multistart=poscidyn.LinearResponse(n_init_cond=16, random_seed=0),
    n_time_steps=128,
    periods_to_retain=2,
    max_steps=8192,
)
result = solver.frequency_sweep(jnp.linspace(0.85, 1.15, 160))

The entries a[i, j, k] and b[i, j, k, l] contribute respectively to the quadratic and cubic restoring force of mode i. In a coupled system, inspect the modal data before collapsing it into a total response.

See define an oscillator for the array conventions and the workflow for interpretation limits.