The classic Lotka-Volterra predator-prey model shows how two coupled populations naturally oscillate: prey grow when predators are scarce, predators then grow on abundant prey, prey then crash, and predators follow — a repeating cycle.
dR/dt = a·R·(1 − R/K_grass) − b·R·W
dW/dt = c·b·R·W − d·W
R = rabbits, W = wolves, K_grass = grass-limited carrying capacity
- Rabbit birth rate — how fast rabbits reproduce when grass is available.
- Wolf hunting rate — how effectively wolves find and catch rabbits.
- Wolf death rate — how quickly wolves starve or die without enough prey.
- Grass regrowth rate — how fast the grazed grassland (green patches) recovers, setting the rabbits' carrying capacity.
This oscillation is not just theory — real data on Canada lynx and snowshoe hare pelts from the Hudson's Bay Company shows almost exactly this 8-11 year boom-bust cycle in the wild.