Intermittency

Period-3 window and intermittent chaos in the logistic map

Clear[x,x0,r,n,nmax]
r=3.8282;nmax=300;

Manipulate[
map=RecurrenceTable[{
x[n+1]==r x[n] (1-x[n]),
x[0]==x0},
x,{n,1,nmax}];
ListLinePlot[map,Mesh->All,PlotMarkers->{"•", 15},DataRange->{0,nmax},PlotRange->{{0,pn},All},AxesLabel->{n,(Subscript[x, n])},LabelStyle->20,ImageSize->600,AspectRatio->0.4],
{{x0,0.05},0,1,0.05,Appearance->"Labeled"},
{{pn,160,"Iterates, n"},30,nmax,Appearance->"Labeled"},
SaveDefinitions->True]

Creation of this notebook was supported by IT Academy program of Information Technology Foundation for Education (HITSA).