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README.md

ManifoldID

This Python package provides various methods for finding influential manifolds in the phase space of 2-dimensional ordinary differential equations (ODEs) that are time independent (extensions to time-dependent systems are currently underway). Some tools available in this package include:

Example Code

The code operates on functions that take in a two-dimensional vector and return a two-dimensional vector .

def myFunction(y):
    ydot = <something>
    return ydot

Next, we can plot, for instance, the phase portrait using phase_plot

import manifoldid as mid
def duffing(y)
    ydot = [y[1] ,y[0]-y[0]**3]
    return ydot
xlims = [-1.5, 1.5]
ylims = [-1, 1]
mid.phase_plot(duffing, xlims, ylims)

Installation

manifoldid will soon be available on pip, but for now, you need to clone the github repository and run the setup.py file.

git clone https://github.com/gknave/ManifoldID.git
cd manifoldid
python setup.py install

To-do List

  1. Parallelize!
    Many methods in this package require the integration of many trajectories over a grid of initial conditions. Parallelizing the code would speed up performance and make it much more useable.

  2. Extend to non-autonomous systems

  3. Extend to experimental data

Contribute

If you would like to be a part of this project moving forward, there's lots to do! Just send me an email at Gary.Nave@colorado.edu, and we can talk about how to make ManifoldID even more awesome!

License

MIT License

Copyright (c) 2018 Gary Nave

This is research code. There will likely be bugs.

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Python package with methods to identify attracting and repelling manifolds, particularly within 2D autonomous ODE models.

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