Lotka Volterra model

The Lotka-Volterra equations, developed in the 1920s by Alfred Lotka and Vito Volterra representing the cyclic, phase-shifted population dynamics between a predator and its prey.

\begin{align*}
  \frac{d Prey}{dt} &= \alpha \cdot Prey - \beta \cdot Predator \cdot Prey \\ 
  \frac{d Predator}{dt} &= \delta \cdot Predator \cdot Prey - \gamma \cdot Predator
\end{align*}