The qualitative analysis of a difference equation of population growth
SummaryThe difference equation fb:[0,1]−[0,1] defined by fb(x)=b x(1−x) is studied. In particular complete qualitative information is obtained for the parameter value b=3.83. For example the number of fixed points of (fb)i is given by 
$$N_i = 1 + \left( {\frac{{1 + \sqrt 5 }}{2}} \right)^i + \left( {\frac{{1 - \sqrt 5 }}{2}} \right)^i$$
