LorenzPy

A Python package to simulate and measure chaotic dynamical systems.

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⚙️ 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

• The main documentation can be found here: https://duncdennis.github.io/lorenzpy/
  • ⚠️: The documentation is not in a useful state.

⚠️ 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. ↩