tsdynamics 5.2.6

Zero-warmup Rust-engine ODE/DDE/SDE integration, discrete maps, and chaos analysis for dynamical systems.

TSDynamics

Dynamical systems in Python: 151 built-in systems, a native Rust integration engine, and a chaos-analysis toolkit — with the simplest system-definition contract anywhere.

You write the math (one symbolic method); TSDynamics lowers it to a native Rust engine and handles integration, Lyapunov spectra, bifurcation diagrams, Poincaré sections, attractors & basins — and even the documentation page for your system.

A built-in Lorenz attractor — integrated, spun, and saved to a GIF (code below).

import tsdynamics as ts

lor = ts.Lorenz()
traj = lor.integrate(final_time=100.0, dt=0.01)
traj["x"]                              # named component access
lor.lyapunov_spectrum()                # → [0.91, ~0, -14.57]
ts.kaplan_yorke_dimension(_)           # → ~2.06

📖 Documentation: https://el3ssar.github.io/TSDynamics/

---

Define your own system

import tsdynamics as ts

class Rossler(ts.ContinuousSystem):
    params = {"a": 0.2, "b": 0.2, "c": 5.7}
    dim = 3
    variables = ("x", "y", "z")            # optional niceties

    @staticmethod
    def _equations(y, t, *, a, b, c):
        x, yv, z = y(0), y(1), y(2)
        return (-yv - z, x + a * yv, b + z * (x - c))

That's the whole contract. The class auto-registers: every analysis tool works on it, the test-suite sweeps it, and the docs build renders its equations (LaTeX, straight from the symbolics) and its attractor — zero extra steps. Delay systems use y(0, t - tau); maps implement _step/_jacobian (signature order validated at import); SDEs add a _diffusion term.

From equations to figures

Every system produces a Trajectory, and every Trajectory knows how to plot itself (to_plot_spec auto-detects the right kind from the data). The plot is a backend-neutral spec you tweak fluently, then render or save to matplotlib, plotly (interactive), or a three.js / JSON export.

Bifurcation diagram of the logistic map, with the period-doubling onsets marked — orbit_diagram is one call, and .bifurcation_points() finds the cascade ($r_1 = 3$, $r_2 = 1 + \sqrt6 \approx 3.449$, …):

import numpy as np, tsdynamics as ts
from tsdynamics.viz import Annotation

orbit = ts.orbit_diagram(ts.Logistic(), "r", np.linspace(2.8, 4.0, 2000))
pts = orbit.bifurcation_points()

spec = orbit.to_plot_spec().relabel(x="r", y="x*", title="Logistic bifurcation")
spec.style(color="k", s=0.2, alpha=0.5)                  # tiny semi-transparent dots
spec.annotations = [
    Annotation("vline", x=pts[i], text=lbl, style={"color": "red", "linestyle": "--"})
    for i, lbl in [(0, " r₁"), (1, " r₂"), (3, " r₄")]
]
spec.save("bifurcation.png", size=(1600, 700))

A PDE, too — the Kuramoto–Sivashinsky equation is a built-in spatially extended system; its space–time field is auto-detected and drawn as a heatmap:

ks = ts.KuramotoSivashinsky(N=128, L=22.0)
traj = ks.integrate(final_time=200.0, dt=0.25)
traj.to_plot_spec().save("ks.png")        # 128-mode space–time field

The spinning attractor at the top is the same to_plot_spec, animated:

traj = ts.Lorenz().integrate(final_time=100.0, dt=0.01)
spec = traj.to_plot_spec()
spec.style(axes=False).trail(None).camera(spin=0.4)      # full curve, no axes, rotate
spec.animate(fps=30, duration=10, loop=True)
spec.save("lorenz.gif")

A taste of the analysis layer

import numpy as np, tsdynamics as ts

# Poincaré section of the Rössler attractor (root-refined crossings)
section = ts.poincare_section(ts.Rossler(), plane=("y", 0.0, "up"), n=500)

# Fixed points of the Hénon map, with stability
ts.fixed_points(ts.Henon())
# [FixedPoint([-1.1314 -0.3394], unstable), FixedPoint([0.6314 0.1894], unstable)]

# Maximal Lyapunov exponent — no Jacobian needed
ts.max_lyapunov(ts.Lorenz(ic=[1, 1, 1]), dt=0.05)        # ≈ 0.9

Plus: attractors & basins of any flow or map, correlation/Rényi fractal dimensions, permutation/sample/dispersion entropy, RQA (recurrence quantification), surrogate hypothesis tests, delay embedding (Takens, optimal τ, Cao/FNN), GALI & the 0–1 chaos test, and Lyapunov exponents from a bare time series (Kantz/Rosenstein).

Highlights

• Three families, one interface

  • ODEs

  • DDEs

  • SDEs

  • Discrete Maps

• 151 built-in systems with literature parameters.

• Native engine: equations lower to a Rust engine (an SSA-tape interpreter, with a Cranelift JIT alongside) in-process; parameters are runtime values, so changing them is free and there is no compile step or cache.

• Composition — a PoincareMap of a flow is a discrete map, so orbit_diagram(PoincareMap(Rossler(), ("y", 0.0)), "c", values) draws the bifurcation diagram of a flow in one line.

• Backend-neutral plotting — one PlotSpec IR renders to matplotlib, plotly (interactive + animated HTML), three.js, or JSON, with a fluent styling/theming vocabulary.

Install

pip install tsdynamics            # or: uv add tsdynamics

A prebuilt abi3 wheel (manylinux / musllinux / macOS / Windows) bundles the native Rust engine. No Rust toolchain and no C compiler needed to install or run. Optional plotting extra: tsdynamics[plot,interactive] (matplotlib, plotly).

Development

git clone https://github.com/El3ssar/TSDynamics && cd TSDynamics
uv sync --group dev --group docs
uv run pytest -m "not slow" --no-cov     # fast tier
uv run pytest --no-cov                   # full local suite
TSD_DOCS_FIGURES=0 uv run mkdocs serve   # docs preview

Releases are automated: conventional-commit PR titles drive semantic-release on merge see CONTRIBUTING.

License

MIT © Daniel Estevez