Malthusian: x' = rx
Solution: x = x₀·e^{rt}
Grows forever, no singularity

Logistic: x' = rx(1-x/K)
Solution: sigmoidal
x → K as t → ∞

Hyperbolic: x' = xᵖ (p>1)
Solution: x = x₀/(1-x₀^{p-1}·(p-1)·t)^{1/(p-1)}
Blowup at t* = 1/(x₀^{p-1}·(p-1))

Hierarchy of growth:
Logistic ≪ Malthus ≪ Hyperbolic