DuncDennis / lorenzpy

A Python package to simulate and measure chaotic dynamical systems.

Home Page:https://duncdennis.github.io/lorenzpy/

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LorenzPy

A Python package to simulate and measure chaotic dynamical systems.

Code style: black Ruff codecov license: MIT Python versions


Flow-Attractors


⚙️ Installation

To install only the core functionality:

$ pip install lorenzpy

To install with the additional plotting functionality. This also installs matplotlib. ⚠️ Plotting functionality not in a useful state.

$ pip install lorenzpy[plot]

▶️ Usage

LorenzPy can be used to simulate and measure chaotic dynamical systems. The following example shows how to simulate the famous Lorenz63 system, and measure its largest Lyapunov exponent from the Lorenz63 iterator:

import lorenzpy as lpy

# Initialize the Lorenz63 simulation object with a RK4 time step of dt=0.05
l63_obj = lpy.simulations.Lorenz63(dt=0.05)

# Simulate 5000 steps of the Lorenz63 system:
data = l63_obj.simulate(5000)    # -> data.shape = (5000,3)

# Calculate the largest Lyapunov exponent from the l63_obj iterator:
iterator = l63_obj.iterate
lle = lpy.measures.largest_lyapunov_exponent(
    iterator_func=iterator,
    starting_point=l63_obj.get_default_starting_pnt(),
    dt=l63_obj.dt
)
# -> lle = 0.905144329...

The calculated largest Lyapunov exponent of 0.9051... is very close to the literature value of 0.90561.

For more examples see the examples folder.

💫 Supported systems

Name Type System Dimension
Lorenz63 autonomous dissipative flow 3
Roessler autonomous dissipative flow 3
ComplexButterfly autonomous dissipative flow 3
Chen autonomous dissipative flow 3
ChuaCircuit autonomous dissipative flow 3
Thomas autonomous dissipative flow 3
WindmiAttractor autonomous dissipative flow 3
Rucklidge autonomous dissipative flow 3
Halvorsen autonomous dissipative flow 3
DoubleScroll autonomous dissipative flow 3
Lorenz96 autonomous dissipative flow variable
DoublePendulum conservative flow 4
Logistic noninvertible map 1
Henon dissipative map 2
SimplestDrivenChaoticFlow conservative flow 2 space + 1 time
KuramotoSivashinsky PDE variable
MackeyGlass delay differential equation variable

📗 Documentation

⚠️ Further notes

  • So far the usefulness of this package is very limited. The authors main purpose to creating this package was to learn the full workflow to develop a Python package. More information about the development process can be found in CONTRIBUTING.md.
  • The plotting functionality, which can be installed with pip install lorenzpy[plot] is not tested so far.
  • See Pynamical for a similar package

Footnotes

  1. Sprott, Julien Clinton, and Julien C. Sprott. Chaos and time-series analysis. Vol. 69. Oxford: Oxford university press, 2003.