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Dynamical Systems Modeling Framework

Project description


License CircleCI PyPI version Documentation Status Python

PyRates is a framework for dynamical systems modeling, developed by Richard Gast and Daniel Rose. It is an open-source project that everyone is welcome to contribute to.

Basic features

Basic features:

  • Frontend:
    • implement models via a frontend of your choice: YAML or Python
    • create basic mathematical building blocks (i.e. differential equations and algebraic equations) and use them to define a networks of nodes connected by edges
    • create hierarchical networks by connecting networks via edges
  • Backend:
    • choose from a number of different backends
    • NumPy backend for dynamical systems modeling on CPUs via Python
    • Tensorflow and PyTorch backends for parameter optimization via gradient descent and dynamical systems modeling on GPUs
    • Julia backend for dynamical system modeling in Julia, via tools such as DifferentialEquations.jl
    • Fortran backend for dynamical systems modeling via Fortran 90 and interfacing the parameter continuation software Auto-07p
    • Matlab backend for differential equation solving via Matlab
  • Other features:
    • perform quick numerical simulations via a single function call
    • choose between different numerical solvers
    • perform parameter sweeps over multiple parameters at once
    • generate backend-specific run functions that evaluate the vector field of your dynamical system
    • Implement dynamic edge equations that include scalar delays or delay distributions (delay distributions are automatically translated into gamma-kernel convolutions)
    • choose from various pre-implemented dynamical systems that can be directly used for simulations or integrated into custom models


Stable release (PyPI)

PyRates can be installed via the pip command. We recommend to use Anaconda to create a new python environment with Python >= 3.6 and then simply run the following line from a terminal with the environment being activated:

pip install pyrates

You can install optional (non-default) packages by specifying one or more options in brackets, e.g.:

pip install pyrates[backends]

Available options are backends, dev, and all at the moment. The latter includes all optional packages. Furthermore, the option tests includes all packages necessary to run tests found in the github repository.

Development version (github)

Alternatively, it is possible to clone this repository and run one of the following lines from the directory in which the repository was cloned:

python install


pip install '.[<options>]'


For a full API of PyRates, see For examplary simulations and model configurations, please have a look at the jupyter notebooks provided in the documenation folder.


If you use this framework, please cite: Gast, R., Rose, D., Salomon, C., Möller, H. E., Weiskopf, N., & Knösche, T. R. (2019). PyRates-A Python framework for rate-based neural simulations. PloS one, 14(12), e0225900.


If you have questions, problems or suggestions regarding PyRates, please contact Richard Gast.

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