f[x_,y_]:=x-y+(x*y-x^3-x*y^2)/Sqrt[x^2 + y^2]
g[x_,y_]:=x+y-(x^2+x^2*y+y^3)/Sqrt[x^2 + y^2]

Manipulate[
   Module[{sol =
    NDSolve[{x'[t]==f[x[t],y[t]],y'[t] == g[x[t],y[t]], x[0] == p[[1]],
    y[0] == p[[2]]}, t,{y,0,T}, {x, 0, T}]},
    ParametricPlot[Evaluate[{x[t], y[t]} /. sol], {t, 0, T},
    PlotRange -> {{-4, 4}, {-3, 3}}]],
    {{p, {2, 1}}, Locator}, {{T, 10}, 0, 100}]