l=100; d4=1.4; d3=1.8; 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},
DisplayFunction->Identity,
PlotPoints->50]
];
max1=4;max2=4;null=0.05;
bild1a=Table[{u0=2 i/max1;v0=2;p},{i,0,max1}];
bild1b=Table[{u0=2;v0=2 j/max1;p},{j,0,max1}];
bild1c=Table[{u0=i/max1;v0=null;p},{i,0,max1}];
oben=0.05;
bild2a=Table[{u0=oben i/max2;v0=oben;p},{i,0,max2}];
bild2b=Table[{u0=oben;v0=oben j/max2;p},{j,0,max2}];
abb0=Show[Evaluate[bild1a,bild1b,bild1c,bild2a,bild2b],
DisplayFunction->$DisplayFunction,
PlotRange->All,AxesLabel->{"u","v"},ImageSize->{400,300}];