The classical way (in all books) is to present the Lotka-Volterra equations:
$$
\begin{align*}
\frac{dH}{dt} &= H(a - b L)\\
\frac{dL}{dt} &= - L(d - c H)
\end{align*}
$$
Here,
- \( H \) is the number of preys
- \( L \) the number of predators
- \( a \), \( b \), \( d \), \( c \) are parameters
Most books quickly establish the model and then use considerable space on
discussing the qualitative properties of this
nonlinear system of
ODEs (which cannot be solved)