Lorenz attractor:
dx/dt = sigma * (y - x) dy/dt = rho * (x - z) - y dz/dt = x * y - beta * z
where sigma = 10, rho = 28 and beta = 8/3.
Python scripts for some 3rd order chaotic systems (Lorenz attractor, Nose-Hoover oscillator, Rossler attractor, Riktake model, Duffing map etc.)
Title | Analysis and modeling chaotic systems |
---|---|
Author | Alexander Kapitanov |
Contact | <email_hidden> |
Project lang | Python 3 |
First Release | 30 May 2019 |
License | GNU GPL 3.0. |
Project requires:
- Python (>= 3.6)
- NumPy (>= 1.19.0)
- SciPy (>= 1.5.1)
- Pandas (>= 1.1.0)
- Matplotlib (>= 3.2.2)
- Pytest (>= 5.4.3)
- Pre-commit (>= 2.6.0)
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.
You can check the latest sources with the command:
$ git clone https://github.com/capitanov/chaospy.git $ cd chaospy $ pip install -r requirements.txt $ python -m src.dynamic_system.py <arguments>
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:
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: 2.6666666666666665 --rho RHO Lorenz system parameter. Default: 28
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