Lotka-Volterra Equations

dx/dt = αx - βxy | dy/dt = δxy - γy

Prey Population

\[\frac{dx}{dt} = \alpha x - \beta xy\]

Growth rate Predation loss

Predator Population

\[\frac{dy}{dt} = \delta xy - \gamma y\]

Reproduction from predation Natural death

System Parameters

α [Prey Growth Rate]

β [Predation Rate]

γ [Predator Death Rate]

δ [Predator Growth Rate]

x₀ [Initial Prey]

y₀ [Initial Predator]

Explore the mathematical foundations and ecological implications of the Lotka-Volterra equations in my detailed Medium article.