Predator and prey

How it works

The model extends the classic Lotka–Volterra equations with grass. Rabbits breed according to the available grass, wolves according to the rabbits they catch, and the grass regrows over time. When rabbits multiply, wolves have more food and their number rises with a delay; then rabbits decline, and later so do wolves. Populations therefore oscillate with a lag or settle into a balance. The “Wolves × rabbits” chart shows this cycle as a loop or spiral.

dR/dt = b_R·G·R − losses − LdW/dt = k·L − m_W·W (L = rabbits caught by wolves)

Try it yourself

1. Run “Finding balance” and watch the “Over time” chart: the peak in wolves comes only after the peak in rabbits.
2. Choose “Rabbits without predators”. Predict what stops the population growing: without wolves, rabbits multiply until the grass runs out.
3. Wait for a steady state and click “☀ 20-day drought”. Watch how long the ecosystem takes to recover.
4. Switch the chart to “Wolves × rabbits” and compare the loops for different starting numbers of wolves.

Model limitations

This is a simplified teaching model: animal numbers change continuously according to equations, and the markers on the map are only an illustration. It includes no inheritance or evolution and does not predict any real ecosystem.

Related experiments

• Galton board
• Ideal gas
• Fractals