Unraveling Predator-Prey Cycles: The Lotka-Volterra Equations
The Lotka-Volterra equations, also known as the Lotka-Volterra predator-prey model, are a pair of first-order nonlinear differential equations often used to describe the dynamics of biological systems where two species interact, one as a predator and the other as prey. The model assumes prey have unlimited food and reproduce exponentially unless preyed upon; the predation rate is proportional to the rate at which predators and prey meet. Predator population growth depends on the predation rate and is affected by natural death rate. The model's solutions are deterministic and continuous, meaning predator and prey generations continuously overlap. The Lotka-Volterra model predicts fluctuating predator and prey population numbers and reveals characteristics of population equilibrium: prey equilibrium density depends on predator parameters, while predator equilibrium density depends on prey parameters. The model has found applications in economics and marketing, describing dynamics in markets with multiple competitors, complementary platforms, and products.