On the stability of the stationary state of a population growth equation with time-lag.

If in the Verhulst equation for population growth the reproduction factor depends on the history then the equilibrium may become unstable and oscillations and even non-constant periodic solutions may occur. It is shown that the equilibrium is unstable if the reproduction factor at time t is, up to a sufficiently large factor, an arbitrary average of the population densities in the interval (t-2, t-1).