In this paper the stability and the asymptotic properties of the population evolution process are considered through the semi-discretization of the continuous population model. We have given the formula of the critical fertility rate of women, and we have shown that the population state is asymptetically stable if the ratio fertility rate is not bigger than the critical fertility rate, and otherwise this state exponentially diverges. Finally, we have obtained the explicit expression of the stationary population state with the critical fertility rate. |