Multistart and synthetic sweeps

Frequency sweeps in Poscidyn are built from independent time integrations, then assembled into selected paths. This is different from numerical continuation, where each solution is explicitly initialized from its immediate predecessor.

Why use multistart?

At one drive frequency, nonlinear systems may admit several stable responses with different basins of attraction. LinearResponse generates a reproducible set of initial displacement and velocity candidates for each requested frequency. TimeIntegration integrates them in a JAX batch, then applies the configured response measure.

This improves the chance of finding different attracting responses, but it does not prove exhaustive branch discovery. Coverage depends on the number and range of initial conditions.

Why select a synthetic path?

Experiments often reveal one response as frequency rises or falls. Once many candidates have been computed independently, NearestNeighbour selects a forward or backward path by preferring nearby response amplitude and phase and discouraging unnecessary seed changes.

The result can be useful for experiment-like plots and parameter studies. It is not a continuation method, a stability computation, or a replacement for bifurcation analysis. Use the nearest-neighbour guide for the selection rule and limitations for the caveats.

What to tune first

1. Validate one representative case with solver.time_response(...).
2. Set enough retained samples for the response features you need.
3. Increase n_init_cond and adjust linear_response_factor to explore candidate coverage.
4. Compare forward and backward paths and check result.stats.

This is the technical background behind the first frequency sweep.