the classic predator-prey model. It begins with two equations. One tracks the prey population, which could be something like the number of bunnies in a forest. The second follows the predator population, which we could imagine as the number of wolves in the same forest. The important point for modelers to capture is that the two populations are tied together. The wolves eat the bunnies, and that changes the bunny population. But eating bunnies lets the wolves reproduce, adding to their population. So, the bunny population affects the wolf population, too. In these linked equations, there’s a part that describes how the bunnies get eaten by wolves, and another that describes how the wolves have more babies by eating bunnies. Eventually, the bunny population peaks as the rapidly growing number of wolves starts having its impact. After that, the bunny numbers drop and they start to grow scarce. The wolf population, however, takes some time to feel the change. Only later do their numbers peak and then start dropping. Eventually, the wolf population gets low enough for the bunnies to recover, and the cycle begins anew.
Adam Frank Light of the Stars: Alien Worlds and the Fate of the Earth