Poincare

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 by following the links in the highlighted titles to open them in the browser or by cloning the dyscolab-tutorials repository to open them locally.

Basics

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

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.

GitHub

Poincare is developed in it's github repo.