sol[r_?NumericQ, U0_?NumericQ] :=
First@NDSolve[{U'[t] == r*(U[t] - U[t]*V[t]),
V'[t] == 1/r*(U[t]*V[t] - V[t]), U[0] == U0, V[0] == U0}, {U,
V}, {t, 0, 20}]
ParametricPlot[
Evaluate[{x[t], y[t]} /. sol[1, #] & /@ Range[0.9, 1.8, 0.1]], {t, 0,
20}, PlotRange -> All, Frame -> True]
Why I am getting empty plot?