d3=4; d6=4; d4=1;
u0=0.006; v0=0.004;
modell:={u'[t]==u[t] (1 - u[t] - d3 v[t]),
         v'[t]==d4 v[t] (1 - v[t] - d6 u[t]),
         u[0]==u0 i, v[0]==v0};
loesung:=NDSolve[modell,{u,v},{t,0,15}];
abb=Plot[Evaluate[Table[{u[t],v[t]}/.loesung,{i,0,1.4,0.2}]],{t,0,15}
                   ,PlotStyle->{{},{Dashing[{0.01}]}}
                   ,AxesLabel->{"t","u,v"}
                   ,PlotRange->All,ImageSize->{400,300}];