Lotka-Volterra Predator-Prey Model Simulator/Calculator

The Lotka-Volterra Model

The Lotka-Volterra equations, also known as the predator-prey equations, are a pair of first-order nonlinear differential equations frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.

Prey Population (x): dx/dt = αx - βxy

• x: number of prey
• α (alpha): natural growth rate of prey in the absence of predation.
• β (beta): predation rate coefficient (effect of predators on prey).

Predator Population (y): dy/dt = δxy - γy

• y: number of predators
• δ (delta): reproduction rate of predators per prey eaten (efficiency of converting prey to predator offspring).
• γ (gamma): natural death rate of predators in the absence of food (prey).

This simulator uses the Euler method for numerical integration to approximate the populations over time.