Boom and Bust

The Lotka–Volterra equations

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Lotka–Volterra: prey grow and get eaten; predators eat and die off.
• Equilibrium at $x^* = \gamma/\delta$, $y^* = \alpha/\beta$.
• Other starting points give endless cycles, with predator peaks lagging prey peaks.

Steps

1. Hares and lynx
2. Find the balance
3. Loops in the plane
4. Orbits in the plane
5. Average over a cycle
6. The rhythm