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Poincare

  • Example 
    import numpy as np
from poincare import *

class LotkaVolterra(System):
    prey: Variable = initial(default=10)
    predator: Variable = initial(default=1)

    prey_eq = prey.derive() << prey * (1 - predator)
    predator_eq = predator.derive() << predator * (prey - 1)

sim = Simulator(LotkaVolterra)
sim.solve(save_at=np.linspace(0, 100, 1000)).to_dataframe().plot()
Lokta-Volterra predator-prey model implemented in Poincare.

Poincare is a python library for declaring and simulating dynamical systems. It's designed around:

  • Modularity: poincare creates a layer to separate the actual declaration and simulation of models, allowing to easily switch between methods and compile to different backends (including NumPy, Numba and JAX).
  • Composability: models are composable, allowing for the combination of smaller systems to create larger ones; complex models can be broken up into more manageable parts.
  • Reproducibility: it intends to be a centralized place for all information concerning models, making it easy to extract data (equations, parameters, etc...) and encouraging consistency between analytical formulations and numerical implementations.
  • Utility: poincare includes a number of utilities to make model analysis more convenient, including searching for steady states, bistability or limit cycles across a range of parameter values.

Installation

It can be installed from PyPI:

pip install -U poincare

or conda-forge:

conda install -c conda-forge poincare

Documentation

Documentation is structured as a series of interactive marimo notebooks which cover basic and advanced topics. They can be ran in the browser either in a static or interactive version or by cloning the dyscolab-tutorials repository to open them locally.

Basics

  • Getting started with Poincare: the essentials necessary to simulate models. Interactive / Static
  • Composition: how to combine smaller models to create more complex ones, one of Poincare's key features. Interactive / Static
  • Simulators: more on how configure the simulation, including switching methods and backends. Interactive / Static

Topic guides

  • Asymptotic behaviour and parameter sweeps: characterize the asymptotic behaviour of the system, including the search for steady states, bistability and limit cycles, across a range of parameter values. Interactive / Static

GitHub

Poincare is developed in it's github repo.