Lotka-Volterra Predator-Prey Model

About the Lotka-Volterra Model

The Lotka-Volterra model (1925-1926) is a cornerstone of mathematical ecology, independently proposed by Italian mathematician Volterra and American mathematician Lotka. It describes periodic population oscillations between predators and prey.

Core equations: dx/dt = ax - bxy (prey rate of change); dy/dt = cxy - dy (predator rate of change). Here a is prey growth rate, b is predation rate, c is conversion efficiency, d is predator death rate.

The phase space plots prey on the x-axis and predators on the y-axis. Classic orbits are closed curves representing periodic oscillations. With density-dependent terms, orbits become spirals—converging or diverging depending on parameters.

This model reveals the inherent oscillation mechanism in ecosystems: more prey → more predators → fewer prey → fewer predators → more prey again. Understanding this cycle is crucial for conservation biology and pest control.