An example: A deterministic analysis of nonlinear effects may mislead!
Kendall (1949) describes an effect discovered by Feller in 1939, which showed that deterministic equations give erroneous results in population models.
has the stationary solution
For convenience, set n1 = 1.
In the limiting case of n2 → ∞, α → 0 while αn2 → λ0, the equilibrium value is
The equilibrium distribution is obtained from the detailed-balance condition 
which yields
where B is the normalizing constant to ensure that the sum of πk from k = n1 to n2 equals one. Now let n2 and α approach their respective limits as above, and n2α approach λ0. Then
This is the result of Feller (1939).