ملف:Lotka-Volterra.svg

tend = 40;
Needs["VectorFieldPlots`"]

Quiet@Manipulate[
  right1 = (a - b y[t]) x[t];
  right2 = (c x[t] - d) y[t];
  Solutions = 
   Table[NDSolve[{x'[t] == right1, y'[t] == right2, x[0] == d/c, 
      y[0] == i}, {x[t], y[t]}, {t, 0, tend}], {i, a/b, 
     3, (3 - a/b)/10}];
  plot1 = 
   ParametricPlot[Evaluate[{x[t], y[t]} /. Solutions], {t, 0, tend}, 
    ImageSize -> {300, 300}, AxesOrigin -> {0, 0}, 
    PlotStyle -> {{Blue, Thick}}];
  plot2 = 
   Plot[Evaluate[{x[t], y[t]} /. Solutions[[-1]]], {t, 0, tend}, 
    ImageSize -> {300, 300}];
  plot3 = ListPlot[{{0, 0}, {d/c, a/b}}, PlotMarkers -> {Automatic}];
  plot4 = 
   VectorFieldPlot[{right1, right2} /. {x[t] -> x, y[t] -> y}, {x, 0, 
     3}, {y, 0, 3}];
  plotLeft = 
   Show[plot1, plot3, plot4, PlotRange -> {{0, 3}, {0, 3}}, 
    AxesLabel -> {x, y}, Ticks -> None];
  Row[{plotLeft, plot2}]
  , {{a, 1}, 0, 5}, {{b, 1}, 0, 5}, {{c, 1}, 0, 5}, {{d, 1}, 0, 5}]