a=0.2;
modell={r'[t]==r[t] (a-r[t]) (r[t]-1),
        w'[t]==1,
        r[0]==r0, w[0]==0};
tmax=50;
p:={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=0.18; p; bild1=bild;
r0=0.22; p; bild2=bild;
r0=2; p; bild3=bild;
bild=Show[bild1,bild2,bild3,DisplayFunction->$DisplayFunction,
ImageSize->{400,300}];