Analysing a model

dynamodels only integrates equations and tracks history; characterizing the resulting signal — is it periodic, quasiperiodic, or chaotic? what is its leading Lyapunov exponent? — is the job of the sibling package ntsa, which works on any model that follows the dynamodels protocol (time_integrate, hist, t_CR, t_transient): every model on this site qualifies without modification.

pip install ntsa

from dynamodels.physical import Lorenz63
from ntsa.characterize import characterize

characterize(Lorenz63(), labels='Lorenz63 (rho=28)', pdf_name='lorenz63_characterization.pdf')

characterize respawns the model, runs it, and produces one diagnostic row per case:

Nonlinear time-series diagnostics for Lorenz63 at \(\rho=28\), left to right: the observable time series, with a zoomed inset; its power spectral density; the 3-D delay-embedded portrait, annotated with the Kaplan-Yorke dimension \(D_{KY}\); the first-return map of the maxima; a plane-crossing Poincare section; a recurrence plot; a 3-D classical-MDS embedding of the full state, coloured by time; and the Lyapunov spectrum, with \(\lambda_1 \approx 0.903\) confirming the classification as chaotic.

Every model page on this site has its own "Nonlinear diagnostics" section with this same row, run for that model's own case — see, for instance, Kuznetsov, where the near-zero leading exponent confirms a quasiperiodic torus rather than chaos despite the broadband-looking time series.

ntsa also exposes classify_regime, bifurcation_sweep and lyapunov_spectrum directly, and its DataSeries class runs the same diagnostics on a signal that was never produced by a dynamodels model — a recorded experiment, for instance. See the ntsa documentation for the full API and theory notes on delay embeddings, regime classification, and Lyapunov spectra.