The Lotka-Volterra equations are a pair of first-order nonlinear differential equations used to describe the dynamics of biological systems in which two species interact, typically a predator and its prey. These equations model how the population of each species changes over time, with the prey population growing in response to food availability and the predator population growing in response to the abundance of prey. The equations are often represented as two equations: one for the prey population, which increases when prey is abundant, and one for the predator population, which increases when there is enough prey to consume. This mathematical model helps ecologists understand population dynamics and the balance of ecosystems.