“the mathematical theory of the struggle for existence.”

The Lotka-Volterra equations are a pair of differential equations that model the changing populations of predators and prey. One equation tracks how prey multiply when predators are scarce, while the other describes how predators prosper when prey are plentiful. Their interaction can produce repeating cycles: prey increase, predators follow, prey decline, and predators then fall behind. The model is deliberately simple, yet it captures the rhythmic push and pull that can emerge when two populations depend on each other. Variations extend the idea to competition and other interacting systems. They are used primarily in ecology, population biology, and mathematical modeling.