Analysis

Analysis

Every quantifier in the toolkit consumes the same System protocol, so the same call works on a map, a flow, or a derived view of a flow. One line each:

import numpy as np
import tsdynamics as ts
from tsdynamics import PoincareMap

# Trajectories — compiled integration / iteration
traj = ts.Lorenz().integrate(final_time=100.0, dt=0.01)
orbit = ts.Henon().iterate(steps=10_000)

# Lyapunov quantifiers
spec = ts.lyapunov_spectrum(ts.Lorenz())                     # ≈ [0.906, 0, -14.57]
lam  = ts.max_lyapunov(ts.Lorenz(ic=[1, 1, 1]), dt=0.05)     # Jacobian-free estimate
d_ky = ts.kaplan_yorke_dimension(spec)                       # ≈ 2.06

# Orbit / bifurcation diagrams
od = ts.orbit_diagram(ts.Logistic(), "r", np.linspace(2.5, 4.0, 600))
od = ts.orbit_diagram(PoincareMap(ts.Rossler(), (1, 0.0)), "c",
                      np.linspace(2.0, 6.0, 80))             # bifurcations of a flow

# Poincaré sections
section = ts.poincare_section(ts.Rossler(), plane=(1, 0.0), steps=500)

# Fixed points of maps, with stability
fps = ts.fixed_points(ts.Henon())

The pages

Page	What it covers
Integrate & iterate	Solvers, tolerances, the Trajectory object, the stepping API
Lyapunov spectra	Spectra per family, max_lyapunov, Kaplan–Yorke dimension, TangentSystem
Orbit & bifurcation diagrams	Parameter sweeps, attractor following, flows via PoincareMap
Poincaré sections	Sections from systems (root-refined) or from trajectory data
Fixed points	Multi-start Newton for maps, eigenvalue stability

For the underlying math — variational equations, QR re-orthonormalization, the Kaplan–Yorke conjecture — see Theory.