l=100; d4=1.4; d3=3.5; d6=4.5;
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;
bild1a=Table[{u0= i/max1;v0=2;p},{i,0,2 max1}];
bild1b=Table[{u0=2;v0=2 j/max1;p},{j,0,max1}];
max2=2;oben=0.05;
bild2a=Table[{u0=oben i/max2;v0=oben;p},{i,0,2 max2}];
bild2b=Table[{u0=oben;v0=oben j/max2;p},{j,0,max2}];
bild3a=Table[{u0= i;v0=2;p},{i,1.035,1.036,0.001}];
bild3b=Table[{u0= i;v0=0.01;p},{i,0.01256,0.01258,0.00002}];
abb0=Show[Evaluate[bild1a,bild1b,bild2a,bild2b,bild3a,bild3b],
DisplayFunction->$DisplayFunction,
PlotRange->All,AxesLabel->{"u","v"},ImageSize->{400,300}];