Chaotic attractors with python (Lorenz, Rossler, Rikitake etc.)
.. -- 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 |
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
Example run::
$ python run.py --showplots --showall lorenz
Dependencies ~~~~
Project requirements: `requirements.txt
Chaotic models ~~~~~~~~
- Lorenz
- Rossler
- Rikitake
- Duffing
- Nose-Hoover
- Lotka-Volterra
- Wang
- Chua
::
usage: parser.py [-h] [-p POINTS] [-s STEP] [--initpoint INITPOINT [INITPOINT ...]] [--showplots] [--saveplots] [--add2d_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. --initpoint INITPOINT [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. --add2dgif 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
