First, clone the repository to a local folder of your choosing.
Package requirements for installation can be found in requirements.txt or environment.yml.
To install requirements using pip, create a new virtual environment. Then run "pip install -r requirements.txt" with the virtual environment active and in the directory of the cloned repository.
See writeup for a more illustrative explanation of the module.
See other writeup to see how I use neural networks to predict dynamical system behavior using TensorFlow.
See generate_signals.ipynb for an example use of the dynamicmodel.py module
The dynamicmodel.py module allows you to simulate a dynamical system and generate signals from it.
You may want to dig into the dynamicmodel.py module itself to see how dynamical systems are constructed from the x_iterate function. A good example is the x_driven function, which calls the x_iterate function.
You may elect to either use your own set of custom "dynamical" functions or use a prebuilt function.
If you elect to use your own system of functions:
- Deftermine your system variables.
- Determine the number of system variables you wish to use. Let's call this number M.
- Define M functions to calculate the system variables' time derivatives as functions of the other variables
- Define an initial state vector of length M, containing the initial values of your variables. There are some conditions for these functions:
- They must take in their respective system variable
- They must take in the time value t
- They must take in a dictionary of custom arguments, called "args". This dictionary can be empty if not needed.
- Pass the following into x_iterate:
- Initial state vector
- The value of the timestep
- The number of timesteps the simulation will iterate through
- A list containing the M functions for the time derivatives
- A dictionary containing the custom arguments required for the system variable functions
Again, reference the x_driven function in dynamicmodel.py to see how this is done.
The following are some plots and "phase portraits" I plotted from my simulation engine.
First I simulate an oscillator with a sinusoidal driving force and a strong damping component:
I also simulate an oscillator with multiple sinusoidal driving forces and a negligible damping component:
