MODELO DISCRETO LOGISTICO

PERIODO DE ORDEN 2

r:=3.2
k:=100

f[x_]:=x*(r-(((r-1)*x)/k))

orbita=NestList[f,3,30]

ListPlot[orbita,PlotStyle->PointSize[0.02]]

ruta=ListPlot[Partition[Flatten[Transpose[{orbita,orbita}]],2,1],PlotJoined->True];
funciones=Plot[{x,f[x]},{x,0,130},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1]},DisplayFunction->Identity];

Show[{ruta,funciones},PlotRange->{{0,130},{0,130}},AxesOrigin->{0.0,0}]

g[x_]:=f[f[x]]

Plot[{g[x],x},{x,0,145}]

NSolve[g[x]==x,x]

g'[x]/.{x->0}
g'[x]/.{x->74.6247}
g'[x]/.{x->100}
g'[x]/.{x->116.284}

orbita1=NestList[g,54,30]

ListPlot[orbita1,PlotStyle->PointSize[0.02]]

orbita2=NestList[g,20,30]

ruta1=ListPlot[Partition[Flatten[Transpose[{orbita1,orbita1}]],2,1],PlotJoined->True];
funciones1=Plot[{x,g[x]},{x,0,130},PlotStyle->{RGBColor[1,0,0],RGBColor[0,0,1]},DisplayFunction->Identity]

Show[{ruta1,funciones1},PlotRange->{{0,130},{0,130}},AxesOrigin->{0.0,0}]

ListPlot[orbita2,PlotStyle->PointSize[0.02]]