(*Created by Rafael Luís: rafaelluis@netmadeira.com
 2016-09-11: adapted for Mathematica v.10 by Ross Moore *)

(* Times series for logistic map *)
Clear[h,x];
f[x_,h_]=h(x-(x^2));
(*recursive definition of the funtion*)
f[x_,h_,0]:=x;
f[x_,h_,n_]:=f[f[x,h,n-1],h]

f[x,1,2]

aa={};
x0=0.1 ; (*initial Value*)
h=3.261205;    (*Parameter*)
iterates=50;
Do[AppendTo[aa,f[x0,h,j]],{j,1,iterates}];
imagem11=ListPlot[aa,Joined->True,AxesLabel->{"n","(Subscript[x, n])"},PlotLabel->StyleForm["Diagaram (n,x(n)) for μ=3.261205"],PlotStyle->{RGBColor[1,0,0]}];

ab={};
x0=0.1 ; (*initial Value*)
h=3.511687;    (*Parameter*)
iterates=50;
Do[AppendTo[ab,f[x0,h,j]],{j,1,iterates}];
imagem11=ListPlot[ab,Joined->True,AxesLabel->{"n","(Subscript[x, n])"},PlotLabel->StyleForm["Diagaram (n,x(n)) for μ=3.511687"],PlotStyle->{Thickness[.002],RGBColor[1,0,0]}]

ac={};
x0=0.1 ; (*initial Value*)
h=3.574940;    (*Parameter*)
iterates=50;
Do[AppendTo[ac,f[x0,h,j]],{j,1,iterates}];
imagem11=ListPlot[ac,Joined->True,AxesLabel->{"n","(Subscript[x, n])"},PlotLabel->StyleForm["Diagram (n,x(n)) for μ=3.574940"],PlotStyle->{RGBColor[1,0,0]},AxesOrigin->{0,0.3}];

ad={};
x0=0.1 ; (*initial Value*)
h=3.683735;    (*Parameter*)
iterates=50;
Do[AppendTo[ad,f[x0,h,j]],{j,1,iterates}];
imagem11=ListPlot[ad,PlotJoined->True,AxesLabel->{"n","(Subscript[x, n])"},PlotLabel->StyleForm["Diagaram (n,x(n)) for μ=3.683735"],PlotStyle->{Thickness[.002],RGBColor[1,0,0]}]

ae={};
x0=0.1 ; (*initial Value*)
h=3.855783;    (*Parameter*)
iterates=50;
Do[AppendTo[ae,f[x0,h,j]],{j,1,iterates}];
imagem11=ListPlot[ae,Joined->True,AxesLabel->{"n","(Subscript[x, n])"},PlotLabel->StyleForm["Diagaram (n,x(n)) for μ=3.855783"],PlotStyle->{Thickness[.002],RGBColor[1,0,0]}]

af={};
x0=0.1 ; (*initial Value*)
h=4;    (*Parameter*)
iterates=50;
Do[AppendTo[af,f[x0,h,j]],{j,1,iterates}];
imagem11=ListPlot[af,Joined->True,AxesLabel->{"n","(Subscript[x, n])"},PlotLabel->StyleForm["Diagram (n,x(n)) for μ=4"],PlotStyle->{Thickness[.002],RGBColor[1,0,0]}]