Predator Prey Equations

This embroidery design is a visualisation of the Lotka–Volterra model, a classic mathematical model used to describe how predator and prey populations (like foxes and rabbits in a shared habitat) interact over time.

This pattern plots the relationship between the populations of the two species directly. The horizontal axis represents the number of prey and the vertical axis represents the number of predators. Each curved loop in the pattern shows how the two populations rise and fall together in a repeating cycle. Mathematicians call this a closed orbit in phase space.

See if you can track this pattern: when there are few predators, the prey population grows rapidly. This abundance of food allows predator numbers to rise. As predators become more numerous, they reduce the prey population. Eventually, prey becomes scarce, and predators begin to die off. With fewer predators around, prey can flourish again.

This repeating behaviour is captured by a pair of differential equations, mathematical expressions that describe how the populations change with time. Each closed loop represents a different starting point, but all follow the same kind of pattern - an endless back-and-forth between predator and prey.