Logistic Growth

Simple logistic population growth with saturation.

Level:Beginner

populationsaturationgrowths-curve

Stocks:population
Flows:growth
Feedback Loops:reinforcing adoption, saturation constraint
Probes:population, growth

Dynamic Behavior Patterns

Explore common system behaviors: exponential growth, goal-seeking decay, overshoot-and-collapse, and S-curve saturation.

Explore Dynamic Behavior Patterns

simulation.py

Watching a population grow logistically

This classic model starts with a small population that grows almost exponentially. Growth then slows as the number of individuals nudges up against the carrying capacity of the environment.


from tys import probe, progress

Simulate logistic population growth.

def simulate(cfg: dict):

    import simpy
    env = simpy.Environment()

    population = cfg["initial_pop"]
    r = cfg["growth_rate"]
    K = cfg["carrying_capacity"]
    steps = cfg["steps"]

    done = env.event()

Evolve the population using the logistic equation.

    def run():
        nonlocal population
        for t in range(steps):
            growth = r * population * (1 - population / K)
            population += growth
            probe("population", env.now, population)
            probe("growth", env.now, growth)
            progress(int(100 * (t + 1) / steps))
            yield env.timeout(1)
        done.succeed({"final_population": population})

    env.process(run())
    env.run(until=done)
    return done.value


def requirements():
    return {
        "builtin": ["micropip", "pyyaml"],
        "external": ["simpy==4.1.1"],
    }

config.yaml

initial_pop: 10
growth_rate: 0.2
carrying_capacity: 100
steps: 40

Goal-Seeking Decay Logistic Map