l=3; d4=1.4; d3=1.1; d6=0.95;
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},
   DisplayFunction->Identity,
   PlotPoints->200]
];
max=2;
bild1a=Table[{u0=max i/max;v0=max;p},{i,0.1,max,0.3}];
bild1b=Table[{u0=max;v0=max j/max;p},{j,0.1,max,0.3}];
bild2a=Table[{u0=max i/max;v0=0.1;p},{i,0.1,max,0.3}];
bild2b=Table[{u0=0.1;v0=max j/max;p},{j,0.1,max,0.3}];
abb0=Show[Evaluate[bild1a,bild1b,bild2a,bild2b],
DisplayFunction->$DisplayFunction,
PlotRange->{{0,2},{0,2}},AxesLabel->{"u","v"},ImageSize->{400,300}];