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https://github.com/hukenovs/chaospy
Chaotic attractors with python (Lorenz, Rossler, Rikitake etc.)
https://github.com/hukenovs/chaospy
attractor attractors chaos chaos-theory chaotic-dynamical-systems chaotic-systems duffing-equation lorenz lorenz-attractor lotka-volterra ode-model python rossler rossler-attractor scipy
Last synced: about 2 months ago
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Chaotic attractors with python (Lorenz, Rossler, Rikitake etc.)
- Host: GitHub
- URL: https://github.com/hukenovs/chaospy
- Owner: hukenovs
- License: gpl-3.0
- Created: 2019-05-30T16:12:40.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2024-01-13T10:23:44.000Z (12 months ago)
- Last Synced: 2024-10-31T08:42:04.655Z (2 months ago)
- Topics: attractor, attractors, chaos, chaos-theory, chaotic-dynamical-systems, chaotic-systems, duffing-equation, lorenz, lorenz-attractor, lotka-volterra, ode-model, python, rossler, rossler-attractor, scipy
- Language: Python
- Homepage:
- Size: 3.77 MB
- Stars: 93
- Watchers: 8
- Forks: 20
- Open Issues: 0
-
Metadata Files:
- Readme: README.rst
- License: LICENSE
Awesome Lists containing this project
README
.. -*- mode: rst -*-
Python scripts for some 3rd-order chaotic systems (Lorenz attractor,
Nose-Hoover oscillator, Rossler attractor, Riktake model, Duffing map etc.)
Chaotic attractors
==================
.. image:: https://raw.githubusercontent.com/capitanov/chaospy/master/img/Lorenz_3d.gif?sanitize=true
Math model::
dx/dt = sigma * (y - x)
dy/dt = rho * x - y - x * z
dz/dt = x * y - beta * z
where sigma = 10, rho = 28 and beta = 8/3.
Main info
~~~~~~~~~
+---------------------+-----------------------------------------+
| **Title** | Analysis and modeling chaotic systems |
+=====================+=========================================+
| **Author** | Alexander Kapitanov |
+---------------------+-----------------------------------------+
| **Contact** | |
+---------------------+-----------------------------------------+
| **Project lang** | Python 3 |
+---------------------+-----------------------------------------+
| **First Release** | 30 May 2019 |
+---------------------+-----------------------------------------+
| **License** | GNU GPL 3.0. |
+---------------------+-----------------------------------------+
Chaotic system
~~~~~~~~~~~~~~~~~~~~~~~~
Rossler attractor::
dx/dt = -(y + z)
dy/dt = x + a * y
dz/dt = b + z * (x - c)
where a = 0.2, b = 0.2 and c = 5.7.
.. image:: https://raw.githubusercontent.com/capitanov/chaospy/master/img/Rossler_3D.png?sanitize=true
Spectrum and auto correlation
****************
.. image:: https://raw.githubusercontent.com/capitanov/chaospy/master/img/Lorenz_Spectrum.png?sanitize=true
Source code
~~~~~~~~~~~
You can check the latest sources with the command::
$ git clone
$ cd chaospy
$
$ conda create -y -n venv python==3.9
$ conda activate venv
$ pip install -r requirements.txt
Example run::
$ python run.py --show_plots --show_all lorenz
Dependencies
~~~~~~~~~~~~
Project requirements: ``requirements.txt``
Chaotic models
~~~~~~~~~~~~~~~~~~~~~~~~
- Lorenz
- Rossler
- Rikitake
- Duffing
- Nose-Hoover
- Lotka-Volterra
- Wang
- Chua
Help
~~~~
::
usage: parser.py [-h] [-p POINTS] [-s STEP]
[--init_point INIT_POINT [INIT_POINT ...]] [--show_plots]
[--save_plots] [--add_2d_gif]
{lorenz,rossler,rikitake,chua,duffing,wang,nose-hoover,lotka-volterra}
...
Specify command line arguments for dynamic system.Calculate some math
parameters and plot some graphs of a given chaotic system.
optional arguments:
-h, --help show this help message and exit
-p POINTS, --points POINTS
Number of points for dymanic system. Default: 1024.
-s STEP, --step STEP Step size for calculating the next coordinates of
chaotic system. Default: 100.
--init_point INIT_POINT [INIT_POINT ...]
Initial point as string of three floats: "X, Y, Z".
--show_plots Show plots of a model. Default: False.
--save_plots Save plots to PNG files. Default: False.
--add_2d_gif Add 2D coordinates to 3D model into GIF. Default:
False.
Chaotic models:
You can select one of the chaotic models:
{lorenz,rossler,rikitake,chua,duffing,wang,nose-hoover,lotka-volterra}
lorenz Lorenz chaotic model
rossler Rossler chaotic model
rikitake Rikitake chaotic model
chua Chua chaotic model
duffing Duffing chaotic model
wang Wang chaotic model
nose-hoover Nose-hoover chaotic model
lotka-volterra Lotka-volterra chaotic model
Chaotic attractors are used as subparse command. Example:
Lorenz attractor
****************
::
usage: parser.py lorenz [-h] [--sigma SIGMA] [--beta BETA] [--rho RHO]
optional arguments:
-h, --help show this help message and exit
Lorenz model arguments:
--sigma SIGMA Lorenz system parameter. Default: 10
--beta BETA Lorenz system parameter. Default: 2.6666
--rho RHO Lorenz system parameter. Default: 28
Chua circuit
************
::
usage: parser.py chua [-h] [--alpha ALPHA] [--beta BETA] [--mu0 MU0]
[--mu1 MU1]
optional arguments:
-h, --help show this help message and exit
Chua model arguments:
--alpha ALPHA Chua system parameter. Default: 0.1
--beta BETA Chua system parameter. Default: 28
--mu0 MU0 Chua system parameter. Default: -1.143
--mu1 MU1 Chua system parameter. Default: -0.714
See Also
~~~~~~~~
- `Wiki `__
- `Habr `__