l=200;
d4=1.4; d3=0.2; d6=0.5;
modell={u'[s]==u[s] (1 - u[s] - d3 v[s]),
         v'[s]==d4 v[s] (1 - v[s] - d6 u[s]),
          u[0]==u0, v[0]==v0};
p:=Module[{},loesung=NDSolve[modell,{u,v},{s,0,l}]; 
    abb=ParametricPlot[Evaluate[{u[s],v[s]}/.loesung],{s,0,l}
                   ,PlotStyle->{Dashing[{abst}]}
                   ,AxesLabel->{"u","v"}
                   ,DisplayFunction->Identity];
  ];
u0=0.01; v0=0.01; abst= 0.01; p; abb1=abb;
u0=2; v0=0.01; abst=0.02; p; abb2=abb;
u0=0.01; v0=2; abst=0.03; p; abb3=abb;
u0=2; v0=2; abst=0.001;   p; abb4=abb;
pkt=ListPlot[{{(-1+d3)/(-1+d3 d6),(-1+d6)/(-1+d3 d6)}},
   DisplayFunction->Identity];
abb0=Show[pkt,abb1,abb2,abb3,abb4,
PlotRange->All,AxesLabel->{"u","v"},
DisplayFunction->$DisplayFunction,ImageSize->{400,300}];