Factor[(m^2)*(1-x)-(m^(3 ))*x*(((1-x))^2)-1==0]

NSolve[1+m-m x-(m^2) x+(m^2) (x^2)==0,x]

Programa para hacer el diagrama de telaraña de la logistica discreta

Needs["GraphicalAnalysis`"]

Aqui se define la funcion, a es parametro

f[x_,a_]:=a*x*(1-x)

PlotIterates[f[x,3.2],{x,0,1},{0.1,0.5},Iterations->500]

PlotIterates[f[x,3.50],{x,0,1},{0.4,0.5},Iterations->500]

PlotIterates[f[x,3.6],{x,0,1},{0.4,0.5},Iterations->100]

PlotIterates[f[x,3.839],{x,0,1},{0.4,0.5},Iterations->100]

Plot[{f[f[x,3.6],3.6],x},{x,0,1},AxesOrigin->{0,0}]

Plot[Fold[f,x,{3.6,3.6,3.6,3.6}],{x,0,1},AxesOrigin->{0,0}]

Bifurcation[f[x,a],{x,0,0.5},{a,2.8,3.9},Iterations->90,Slices->150]