scikit-complexity

A Python library to create and simulate complex systems

scikit-complexity is a Python library to create and simulate complex systems. You describe a model in a few lines, and it works out the mathematics, picks a solver and runs the simulation.

It handles differential equations, stochastic processes, discrete maps, cellular automata, agents, networks and fields through one interface. There are two ways to use it.

The first is the model catalog in skcomplex.models. Pick a ready-made model and run it:

from skcomplex.models import describe, run

print(describe('lotka_volterra').description)

trajectory = run('lotka_volterra').trajectory_
print(trajectory.names)

Prey and predators whose populations oscillate through predation.
['prey.n', 'predators.n', 'growth.r', 'predation.a', 'predation.b', 'death.d']

The second is skcomplex.core, for your own models. A model is made of elements, which carry state, and interactions, which change that state through laws. Here is the same kind of predator and prey system, written from scratch:

from skcomplex.core.elements import CompartmentElement
from skcomplex.core.interactions import RateInteraction
from skcomplex.core.system import System
from skcomplex.engine.runtime import Simulation
system = System(
    elements=[CompartmentElement('rabbits', n=40), CompartmentElement('foxes', n=9)],
    interactions=[
        RateInteraction('r', target='rabbits', state='n', sources=['foxes'],
            rate=lambda s: 1.1 * s.target.n - 0.4 * s.target.n * s.sources[0].n),
        RateInteraction('f', target='foxes', state='n', sources=['rabbits'],
            rate=lambda s: 0.1 * s.target.n * s.sources[0].n - 0.4 * s.target.n),
    ],
)
trajectory = Simulation(system, dt=0.05).check().prepare().run(until=30).trajectory_
print(round(float(trajectory.values('rabbits.n').max())))

53

That is the highest rabbit population reached during the run.

You don’t have to state what kind of model you are building. You write the laws, and the library decides whether it is an ODE, an SDE or a jump process. Add a RerunObserver and the run streams live to the Rerun viewer, where you can watch it while changing its parameters.

The catalog is listed in the gallery, from Game of Life to Schelling segregation. Its models use the same public classes you do, so each one doubles as an example for your own.

Install it with pip install scikit-complexity. It runs on Linux and on macOS with Apple silicon, and on Windows through WSL.