$$x(k+1) = \lambda x(k)[1-x(k)]$$

• $k$, population growth cycle
• $\lambda$, linked to the rate of population growth
• $0 <= x(k) <= 1$, state variable proportional to the number of individuals in the population

In order for $x$ to remain bounded, it should be $0<=\lambda<=4$.

The logistic law describes well the dynamics of evolving populations where there is a growth per cycle proportional to $\lambda x(k)$ with a corrective negative term (feedback) $-\lambda x^2(k)$ which is proportional to the square of the size already attained by the population.