Lotkan ja Volterran DY

Needs["VectorFieldPlots`"]

a=1;b=1;c=1;d=1;

lvkentta=VectorFieldPlot[{a x-b x y ,-c y+d x y},{x,0,3},{y,0,3}] ;

Show[p6,AxesLabel->{"r","h"},Axes->True]

lvdy[x0_,y0_]:=NDSolve[{x'[t]==a x[t]-b x[t] y[t],y'[t]==-c y[t]+ d x[t] y[t],x[0]==x0,y[0]==y0},{x[t],y[t]},{t,0,100}];

ratk[1]=lvdy[.3,1];ratk[2]=lvdy[2,1];

lvrata=ParametricPlot[Evaluate[Table[{x[t],y[t]}/.ratk[i],{i,2}]],{t,0,5}, PlotRange->{{-3,3},{-3,3}}, PlotPoints->100,AxesLabel->{"x","y"},PlotStyle->Thickness[0.005]]

Show[{lvkentta,lvrata,Graphics[{PointSize[.02],Point[{.3,1}]}],Graphics[{PointSize[.02],Point[{1,1}]}],Graphics[{PointSize[.02],Point[{2,1}]}]},PlotRange->{{0,3},{0,3}},AxesLabel->{"x","y"},Axes->True]

lvrata2=ParametricPlot[Evaluate[Table[{x[t],y[t]}/.ratk[i],{i,2}]],{t,0,6.8}, PlotRange->{{-3,3},{-3,3}}, PlotPoints->100,AxesLabel->{"x","y"},PlotStyle->Thickness[0.005]]

Show[{lvkentta,lvrata2,Graphics[{PointSize[.02],Point[{.3,1}]}],Graphics[{PointSize[.02],Point[{1,1}]}],Graphics[{PointSize[.02],Point[{2,1}]}]},PlotRange->{{0,3},{0,3}},AxesLabel->{"x","y"},Axes->True]

Toinen tapa vektorikentälle

lvkentta2=VectorPlot[{a x-b x y ,-c y+d x y},{x,0,3},{y,0,3},VectorPoints->Fine,VectorScale->Medium] ;

Show[{lvkentta2,lvrata2,Graphics[{PointSize[.02],Point[{.3,1}]}],Graphics[{PointSize[.02],Point[{1,1}]}],Graphics[{PointSize[.02],Point[{2,1}]}]},PlotRange->{{0,3},{0,3}},AxesLabel->{"x","y"},Axes->True]

lvkentta2=VectorPlot[{a x-b x y ,-c y+d x y},{x,0,3},{y,0,3},VectorPoints->Fine,VectorScale->Medium,StreamPoints->10]