x[t_]:=Cos[t];
y[t_]:=Sin[t];
a=0.2;u=0.9;
s=0.1+14 Pi/36;
bild1=ParametricPlot[{x[t],y[t]},{t,0,2 Pi},DisplayFunction->Identity];
bild2=ParametricPlot[{a x[t],a y[t]},{t,0, 2 Pi},DisplayFunction->Identity];
bild3=ListPlot[{{x[s],y[s]},{x[s],y[s]-u}},
            PlotJoined->True,DisplayFunction->Identity];
bild4=ListPlot[{{x[s],y[s]-u}},DisplayFunction->Identity];
modell={r'[t]==r[t] (a-r[t]) (r[t]-1),
        w'[t]==1,
        r[0]==r0, w[0]==w0};
tmax=50;
p:=Module[{},{loesung=NDSolve[modell,{r,w},{t,0,tmax},MaxSteps->500];
bild=ParametricPlot[Evaluate[{r[t] Cos[w[t]],
                              r[t] Sin[w[t]]}/.loesung],{t,0,tmax},
PlotRange->All, DisplayFunction->Identity,
AxesLabel->{"x","y"}]
}];
r0=Sqrt[x[s]^2+(y[s]-u)^2];
w0=ArcTan[(y[s]-u)/x[s]];
p; bild5=bild;
bild=Show[bild1,bild2,bild3,bild4,bild5,
DisplayFunction->$DisplayFunction,
ImageSize->{400,300}];