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What are libraries available in Python for the simulation and bifurcation study of dynamical systems?

I want to simulate a model based on four or five ODEs, and build bifurcation maps, based on two parameters. For this I need time series of 40000 data points to classify the morphology for each point in parameter space. Speed matters even though I have access to a cluster with Python.

I know PyDSTool; is there another alternative?

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I authored a Python module named JiTCODE, which is intended for the dynamical-systems community. Here are some features or missing features that my be relevant for you:

  • The right-hand site of the differential equation is just-in-time-compiled, which makes integration rather fast. For smaller systems such as yours, there may still be a relevant overhead though (as compared to a pure C program, for example). Its performance is comparable or better than that of PyDSTool (see Fig. 5 in the accompanying paper).

  • It allows you to change control parameters at run-time, thus avoiding frequent re-compilation when scanning a parameter space.

  • It neither offers dedicated tools for detecting and determining the type of bifurcations nor continuisation. However, since the input is symbolic, it is not a big step to use symbolic equation solvers to find fixed points and determine their stability.

  • It does allow you to almost automatically determine regular and transversal Lyapunov exponents.

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You could install Netlogo. It is a free java-based GUI tool, but it has some language bindings for "remote-controlling" it and fetching the results. It has a large models-library with lots of useful and preconfigured models, some of which might suit your needs.

In this post on SO someone mentions a new Python API, PyNetLogo, but I haven't used that API yet and cannot tell how good it is.

  • Thanks, I will have a look with more attention, but I was maybe looking for something more specific to ODE – Dadep May 2 '18 at 14:41

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