Predator-Prey (Lotka–Volterra, SimPy)
Discrete-time SimPy approximation of the predator–prey model.
Level: Intermediate
simulation.py
Predator and prey via SimPy
This example approximates the Lotka--Volterra equations in discrete time using SimPy's event loop. It intentionally avoids SciPy's ODE solver so it can run in environments where SciPy is unavailable.
Limitations: because we update the populations at a fixed time step, results
depend heavily on the chosen time_step and may drift from the true
continuous solution. A stiff system or a large step size can cause the
simulation to diverge or behave unrealistically.
from tys import probe, progress
def simulate(cfg: dict):
"""Simulate predator and prey populations with SimPy."""
import simpy
env = simpy.Environment()
Parameters
prey = float(cfg["initial_prey"])
predator = float(cfg["initial_predator"])
alpha = cfg["alpha"]
beta = cfg["beta"]
delta = cfg["delta"]
gamma = cfg["gamma"]
sim_time = float(cfg["sim_time"])
dt = float(cfg.get("time_step", 0.01))
assert all(p > 0 for p in (alpha, beta, delta, gamma)), "Rates must be positive"
assert dt > 0 and sim_time > 0, "Time parameters must be positive"
steps = int(sim_time / dt)
done = env.event()
Discretely integrate the differential equations using Euler's method. This simple integrator is convenient but inaccurate for larger dt.
def dynamics():
nonlocal prey, predator
for i in range(steps):
prey_births = alpha * prey
predations = beta * prey * predator
predator_births = delta * prey * predator
predator_deaths = gamma * predator
prey += (prey_births - predations) * dt
predator += (predator_births - predator_deaths) * dt
prey = max(prey, 0.0)
predator = max(predator, 0.0)
probe("prey", env.now, prey)
probe("predator", env.now, predator)
progress(int(100 * (i + 1) / steps))
yield env.timeout(dt)
done.succeed({
"final_prey": prey,
"final_predator": predator,
})
env.process(dynamics())
env.run(until=done)
return done.value
def requirements():
return {
"builtin": ["micropip", "pyyaml"],
"external": ["simpy==4.1.1"],
}
Default.yaml
initial_prey: 10
initial_predator: 5
alpha: 1.5
beta: 1.0
delta: 1.0
gamma: 3.0
sim_time: 20
time_step: 0.01
Charts (Default)
Final Results (Default)
| Metric | Value |
|---|---|
| final_prey | 0.24 |
| final_predator | 10.79 |
FAQ
- Why avoid SciPy in this implementation?
- The populations are stepped forward with Euler integration inside SimPy so it can run even when SciPy is unavailable.
- How does the time_step affect accuracy?
- A larger dt leads to bigger numerical errors since Euler integration is only first order.
- Where is env.timeout used?
- Each discrete step yields env.timeout(dt) to advance the SimPy clock.