TSDynamics

149 built-in dynamical systems. Compiled integration. Chaos analysis.

TSDynamics is a Python library for studying dynamical systems: continuous flows, delay equations, and discrete maps, all behind one interface. You define the math in a single symbolic method; the library compiles it to native code, caches the binary, and gives you trajectories, Lyapunov spectra, bifurcation diagrams, Poincaré sections, and fixed points.

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()    # ≈ [0.906, 0, -14.57]

The first call compiles the right-hand side to a C extension; every later call — in this session or the next — reuses the cached binary.

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Why TSDynamics

• Compiled, not interpreted

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  ODEs and DDEs are compiled to C via JiTCODE / JiTCDDE; discrete maps are JIT-compiled with Numba. Compilation happens once per system class and is cached on disk — parameter changes cost nothing for ODEs.

• 149 systems out of the box

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  118 continuous flows, 5 delay systems, and 26 discrete maps, from Lorenz and Rössler to Mackey–Glass and Hénon — each with literature defaults, named variables, and known Lyapunov values where published.

• One protocol, every analysis

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  Everything that steps — a map, a flow, a Poincaré section of a flow — implements the same System protocol, so the analysis toolkit composes: an orbit diagram over a Poincaré map is a bifurcation diagram.

• Define a system in ten lines

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  Subclass one of three base classes, declare a params dict and dim, write one method. Your class auto-registers, the test suite sweeps it, and its documentation page is generated from the code.

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Where to go

You want to	Go to
Install and run your first trajectory	Start
Browse the built-in systems	Systems
Lyapunov spectra, bifurcation diagrams, sections	Analysis
Understand the compilation cache and the math	Theory
Look up an exact signature	Reference
Contribute a system	Project