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 based on their interactions, with the prey population growing and the predator population declining when prey is abundant. The equations are foundational in the field of ecology and help researchers understand population cycles and stability. They illustrate how changes in one species can significantly impact another, providing insights into the balance of ecosystems and the effects of environmental changes.