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Tip: If the simulation looks noisy, reduce Δt or increase t_max. The delay differential equation is approximated
here using RK4 with linear interpolation for the delay term.
A Lotka-Volterra type model with an Ivlev functional response and gestation delay.
$$ \frac{dx}{dt} = r \cdot x \cdot \left(1 - \frac{x}{K}\right) - \alpha \cdot y \cdot \left(1 - e^{-\beta x}\right) $$
$$ \frac{dy}{dt} = -s \cdot y + Y \cdot \alpha \cdot y(t-\tau) \cdot e^{-s\tau} \cdot \left(1 - e^{-\beta x(t-\tau)}\right) $$