c1=1; c2= 1; c3=2; c4=0.1; c5=0.1; c6=1;
b0=0.6;r0=0.3;l=200;abst=0.01;
modell:={b'[t]==b[t] (c1 (1 - b[t]/c2) - (c3 r[t])/(b[t] + c4) ),
        r'[t]==r[t] c5 ( 1 - (c6 r[t])/b[t] ),
        b[0]==b0, r[0]==r0};
loesung=NDSolve[modell,{b,r},{t,0,l}]; 
    abb=ParametricPlot[Evaluate[{b[t],r[t]}/.loesung],{t,0,l}
                   ,PlotStyle->{Dashing[{0.01}]}
                   ,AxesLabel->{"b","r"}
                   ,DisplayFunction->Identity];
abb1=abb;
b0=0.084; r0=0.085;  
loesung=NDSolve[modell,{b,r},{t,0,l}]; 
    abb=ParametricPlot[Evaluate[{b[t],r[t]}/.loesung],{t,0,l}
                   ,PlotStyle->{Dashing[{0.02}]}
                   ,AxesLabel->{"b","r"}
                   ,DisplayFunction->Identity];

abb2=abb;
abb3=Show[abb1,abb2,ImageSize->{400,300},
  DisplayFunction->$DisplayFunction];