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differential equations - Clicking phase plane with mouse


Here is what I have thus far:


SetOptions[VectorPlot,
  VectorScale -> {0.045, .9, None},
  Axes -> True,

  AxesLabel -> {x, y},
  VectorPoints -> 16,
  VectorStyle -> {GrayLevel[0.8]}];
SetOptions[ContourPlot,
  ContourStyle -> {Orange, Green}];
SetOptions[ParametricPlot,
  PlotStyle -> Blue];

I made the above an initialization cell. Next, I have this:


Manipulate[

 Module[{f, g, tmin, tmax, xmin, xmax, ymin, ymax},
  tmin = -2; tmax = 2;
  xmin = -2; xmax = 4;
  ymin = -4; ymax = 2;
  f[x_, y_] = 2 x - y + 3 (x^2 - y^2) + 2 x y;
  g[x_, y_] = x - 3 y - 3 (x^2 - y^2) + 3 x y;
  ptRules = NSolve[{f[x, y] == 0, g[x, y] == 0}, {x, y}];
  z = NDSolveValue[{{x'[t], y'[t]} == {f[x[t], y[t]], 
         g[x[t], y[t]]}, {x[0], y[0]} == #}, {x[t], y[t]}, {t, tmin, 
       tmax}] & /@ u;

  Show[
   VectorPlot[{f[x, y], g[x, y]}, {x, xmin, xmax}, {y, ymin, ymax}],
   ContourPlot[{f[x, y] == 0, g[x, y] == 0}, {x, xmin, xmax}, {y, 
     ymin, ymax}],
   Graphics[{Red, PointSize[Large], Point[{x, y}] /. ptRules}],
   ParametricPlot[z, {t, tmin, tmax}]]],
 {{u, {}}, Locator, Appearance -> None, LocatorAutoCreate -> All},
 {z, {}, None}, Paneled -> False]

Running the manipulate gives this image.



enter image description here


Now use your mouse to click anywhere in the phase plane vector field and a solution trajectory will be drawn.


Now my question. Each time I click in the vector field, it shrinks, then expands, then draws. Can anything be done to stop this motion (shrink, expand on each click)?


Second question: The cell indicators on the right margin are blinking. What's up with that?




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