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How to plot and manipulate eigenvalues when changing parameters ?

Hello everybody,

I am working with a very complex non-linear differential system. I would like to start to examine the stability of the solutions in the easy case of only 3 species and 22 parameters (3 differential equations). I called this system: Benesystem. I created the jacobian matrix and extracted the eigen values. I called these eigen.
Now I would like to create a plot showing the real parts and imaginary parts of each eigen values for the solutions of the system for each values of the 22 parameters. In other words, I want to examine how the parameters influence the eigenvalues and therefore the stability of the solutions. I am still learning how to use mathematica so I am having some hard time creating such a plot.


Thank you for your help!
Bene

Here is the code I am using. 

Manipulate[ Module[  {soln, col1 = RGBColor[1, .47, 0],    col2 = ColorData["HTML", "SlateBlue"],    col3= ColorData["HTML", "Black"]},  Plot[Evaluate[{Re[eigen /. {#[[1]], #[[2]],  #[[3]]}],        Im[eigen /. {n1 = #[[1]], y = #[[2]], m = #[[3]]}] } &[     soln = Quiet@       Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1, mm1, p1,          p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1, rm}, {species10,          species20, species30}, tmax]]]   , {t, 0, Min[tmax, Min[#[[1, 1, 2]] & /@ soln]]},   AxesLabel ->     TraditionalForm /@ {t, {Style[e1, col1], Style[e2, col2],        Style[e3, col3]}},   PlotRange -> All, AxesOrigin -> {0, 0},    PlotStyle -> {col1, col2, col3}, ImageSize -> {500, 500},    ImagePadding -> {{40, 10}, {10, 25}}]  ], {{b1, 1, "b1"}, 0, 2, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{a11, 1, "a11"}, 0, 1, .01,   ImageSize -> Tiny, Appearance -> "Labeled"}, {{f11, 1, "f11"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{f1, 1, "f1"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{h1, 1, "h1"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{g11, 1, "g11"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{p1, 1, "p1"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{p11, 1, "p11"}, 0.1, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{d1, 1, "d1"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{g1, 1, "g1"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{k1, 1, "k1"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{mm1, 1, "mm1"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{fm11, 1, "fm11"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{fm1, 1, "fm1"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{hm1, 1, "hm1"}, 0.1, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{gm1, 1, "gm1"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{gm11, 1, "gm11"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{km1, 1, "km1"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{e, 1, "e"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{r, 1, "r"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, {{rm, 1, "rm"}, 0, 1, .01, ImageSize -> Tiny,   Appearance -> "Labeled"}, Delimiter, "initial populations", {{species10, 1, "species10"}, 0, 10, ImageSize -> Tiny}, {{species20, 1, "species20"}, 0, 10,   ImageSize -> Tiny}, {{species30, 1, "species30"}, 0, 10,   ImageSize -> Tiny}, {{t, 1, "time"}, 0, 10, ImageSize -> Tiny}, SaveDefinitions -> True, ControlPlacement -> Left]
POSTED BY: Bene Bachelot
6 Replies
Thank you Bruce!

I got it to work but then it was plotting each values (imaginary and real parts of the three eigenvalues) over time. Which is interesting but not what I meant to do exactly.. I was thinking just plotting the imaginary and real parts at a given time for a given set of parameters. I rectified the code using a ListPlot instead. It seems to work except that it does not plot anything!!!! Somtimes, I get a message saying the input value lies outside the range of data and the plot remains empty. I am not really sure why it is not plotting any values.
Do you have any idea?


  Manipulate[
   Module[{soln, col1 = RGBColor[1, .47, 0],
     col2 = ColorData["HTML", "SlateBlue"],
     col3 = ColorData["HTML", "Black"]},
    ListPlot[{{Evaluate[{Re[
           eigen /. {n1 -> #[[1]][t], y -> #[[2]][t], m -> #[[3]][t],
               b1 -> b1, a11 -> a11, f11 -> f11, f1 -> f1, h1 -> h1,
               g11 -> g11, g1 -> g1, k1 -> k1, mm1 -> mm1, p1 -> p1,
               p11 -> p11, d1 -> d1, e -> e, r -> r, fm11 -> fm11,
              fm1 -> fm1, hm1 -> hm1, gm11 -> gm11, gm1 -> gm1,
              km1 -> km1, rm -> rm} &[
           soln = Quiet@
             Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1, mm1,
               p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
               rm}, {n10, m0, y0}, t]]]}][1],
      Evaluate[{Im[
          eigen /. {n1 -> #[[1]][t], y -> #[[2]][t], m -> #[[3]][t],
              b1 -> b1, a11 -> a11, f11 -> f11, f1 -> f1, h1 -> h1,
              g11 -> g11, g1 -> g1, k1 -> k1, mm1 -> mm1, p1 -> p1,
              p11 -> p11, d1 -> d1, e -> e, r -> r, fm11 -> fm11,
              fm1 -> fm1, hm1 -> hm1, gm11 -> gm11, gm1 -> gm1,
              km1 -> km1, rm -> rm} &[
          
           soln = Quiet@
             Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1, mm1,
               p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
               rm}, {n10, m0, y0}, t]]]}][
       1]}, {Evaluate[{Re[
          eigen /. {n1 -> #[[1]][t], y -> #[[2]][t], m -> #[[3]][t],
              b1 -> b1, a11 -> a11, f11 -> f11, f1 -> f1, h1 -> h1,
              g11 -> g11, g1 -> g1, k1 -> k1, mm1 -> mm1, p1 -> p1,
              p11 -> p11, d1 -> d1, e -> e, r -> r, fm11 -> fm11,
              fm1 -> fm1, hm1 -> hm1, gm11 -> gm11, gm1 -> gm1,
              km1 -> km1, rm -> rm} &[
           soln = Quiet@
             Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1, mm1,
               p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
               rm}, {n10, m0, y0}, t]]]}][2],
      Evaluate[{Im[
          eigen /. {n1 -> #[[1]][t], y -> #[[2]][t], m -> #[[3]][t],
              b1 -> b1, a11 -> a11, f11 -> f11, f1 -> f1, h1 -> h1,
              g11 -> g11, g1 -> g1, k1 -> k1, mm1 -> mm1, p1 -> p1,
              p11 -> p11, d1 -> d1, e -> e, r -> r, fm11 -> fm11,
              fm1 -> fm1, hm1 -> hm1, gm11 -> gm11, gm1 -> gm1,
              km1 -> km1, rm -> rm} &[
           soln = Quiet@
             Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1, mm1,
               p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
               rm}, {n10, m0, y0}, t]]]}][
       2]}, {Evaluate[{Re[
          eigen /. {n1 -> #[[1]][t], y -> #[[2]][t], m -> #[[3]][t],
              b1 -> b1, a11 -> a11, f11 -> f11, f1 -> f1, h1 -> h1,
              g11 -> g11, g1 -> g1, k1 -> k1, mm1 -> mm1, p1 -> p1,
              p11 -> p11, d1 -> d1, e -> e, r -> r, fm11 -> fm11,
              fm1 -> fm1, hm1 -> hm1, gm11 -> gm11, gm1 -> gm1,
              km1 -> km1, rm -> rm} &[
           soln = Quiet@
             Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1, mm1,
               p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
               rm}, {n10, m0, y0}, t]]]}][3],
      Evaluate[{Im[
          eigen /. {n1 -> #[[1]][t], y -> #[[2]][t], m -> #[[3]][t],
              b1 -> b1, a11 -> a11, f11 -> f11, f1 -> f1, h1 -> h1,
              g11 -> g11, g1 -> g1, k1 -> k1, mm1 -> mm1, p1 -> p1,
              p11 -> p11, d1 -> d1, e -> e, r -> r, fm11 -> fm11,
              fm1 -> fm1, hm1 -> hm1, gm11 -> gm11, gm1 -> gm1,
              km1 -> km1, rm -> rm} &[
           soln = Quiet@
             Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1, mm1,
               p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
               rm}, {n10, m0, y0}, t]]]}][3]}},
    AxesLabel ->
     TraditionalForm /@ {{Style[e1, col1], Style[e2, col2],
        Style[e3, col3]}}, PlotRange -> All, AxesOrigin -> {0, 0},
    PlotStyle -> {col1, col2, col3}, ImageSize -> {500, 500},
    ImagePadding -> {{40, 10}, {10, 25}}]], {{b1, 1, "b1"}, 0, 2, .01,
   ImageSize -> Tiny, Appearance -> "Labeled"}, {{a11, 1, "a11"}, 0,
   1, .01, ImageSize -> Tiny,
   Appearance -> "Labeled"}, {{f11, 1, "f11"}, 0, 1, .01,
   ImageSize -> Tiny, Appearance -> "Labeled"}, {{f1, 1, "f1"}, 0,
   1, .01, ImageSize -> Tiny, Appearance -> "Labeled"}, {{h1, 1, "h1"},
    0, 1, .01, ImageSize -> Tiny,
   Appearance -> "Labeled"}, {{g11, 1, "g11"}, 0, 1, .01,
   ImageSize -> Tiny, Appearance -> "Labeled"}, {{p1, 1, "p1"}, 0,
   1, .01, ImageSize -> Tiny,
   Appearance -> "Labeled"}, {{p11, 1, "p11"}, 0.1, 1, .01,
   ImageSize -> Tiny, Appearance -> "Labeled"}, {{d1, 1, "d1"}, 0,
   1, .01, ImageSize -> Tiny, Appearance -> "Labeled"}, {{g1, 1, "g1"},
    0, 1, .01, ImageSize -> Tiny,
   Appearance -> "Labeled"}, {{k1, 1, "k1"}, 0, 1, .01,
   ImageSize -> Tiny, Appearance -> "Labeled"}, {{mm1, 1, "mm1"}, 0,
   1, .01, ImageSize -> Tiny,
   Appearance -> "Labeled"}, {{fm11, 1, "fm11"}, 0, 1, .01,
   ImageSize -> Tiny, Appearance -> "Labeled"}, {{fm1, 1, "fm1"}, 0,
   1, .01, ImageSize -> Tiny,
   Appearance -> "Labeled"}, {{hm1, 1, "hm1"}, 0.1, 1, .01,
   ImageSize -> Tiny, Appearance -> "Labeled"}, {{gm1, 1, "gm1"}, 0,
   1, .01, ImageSize -> Tiny,
   Appearance -> "Labeled"}, {{gm11, 1, "gm11"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{km1, 1, "km1"}, 0,
  1, .01, ImageSize -> Tiny, Appearance -> "Labeled"}, {{e, 1, "e"},
  0, 1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{r, 1, "r"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{rm, 1, "rm"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, Delimiter, "initial populations", {{n10,
   1, "species10"}, 0, 10, ImageSize -> Tiny}, {{m0, 1, "species20"},
  0, 10, ImageSize -> Tiny}, {{y0, 1, "species30"}, 0, 10,
  ImageSize -> Tiny}, {{t, 1000, "maximum time"}, 1, 1000,
  ImageSize -> Tiny}, SaveDefinitions -> True,
ControlPlacement -> Left]
POSTED BY: Bene Bachelot
The options-expected warning came because you have the expressions to plot in the
first two argumenrts, not just the first argument.  Enclosing them in curly braces ({..})
makes them one argument.
 Plot[ {Evaluate[{Re[
      eigen /. {n1 -> #[[1]], y -> #[[2]], m -> #[[3]], b1 -> b1,
          a11 -> a11, f11 -> f11, f1 -> f1, h1 -> h1, g11 -> g11,
          g1 -> g1, k1 -> k1, mm1 -> mm1, p1 -> p1, p11 -> p11,
          d1 -> d1, e -> e, r -> r, fm11 -> fm11, fm1 -> fm1,
          hm1 -> hm1, gm11 -> gm11, gm1 -> gm1, km1 -> km1,
          rm -> rm} &[
       soln = Quiet@
         Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1, mm1, p1, p11,
          d1, e, r, fm11, fm1, hm1, gm11, gm1, km1, rm}, {species10,
          species20, species30}, tmax]]]}],
  Evaluate[{Im[
     eigen /. {n1 -> #[[1]], y -> #[[2]], m -> #[[3]], b1 -> b1,
         a11 -> a11, f11 -> f11, f1 -> f1, h1 -> h1, g11 -> g11,
         g1 -> g1, k1 -> k1, mm1 -> mm1, p1 -> p1, p11 -> p11,
         d1 -> d1, e -> e, r -> r, fm11 -> fm11, fm1 -> fm1,
         hm1 -> hm1, gm11 -> gm11, gm1 -> gm1, km1 -> km1,
         rm -> rm} &[
      soln = Quiet@
        Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1, mm1, p1, p11,
          d1, e, r, fm11, fm1, hm1, gm11, gm1, km1, rm}, {species10,
          species20, species30}, tmax]]]}]}, {t, 0,
  Min[tmax, Min[#[[1, 1, 2]] & /@ soln]]}
There is a problem with the
Min[tmax, Min[#[[1, 1, 2]] & /@ soln]]
I think (haven't investigated deeply) that tmax does not have a value yet when the Plot is starting.
POSTED BY: Bruce Miller
Thank you Michael,
This seems to help a little. Now I can see that Mathematica is trying to incorporate the right parameter values in the eigenvalues. The plot doesn't work though, it says an option in Plot is expected. 
 Manipulate[
  Module[{soln, col1 = RGBColor[1, .47, 0],
    col2 = ColorData["HTML", "SlateBlue"],
    col3 = ColorData["HTML", "Black"]},
   Plot[Evaluate[{Re[
       eigen /. {n1 -> #[[1]], y -> #[[2]], m -> #[[3]], b1 -> b1,
           a11 -> a11, f11 -> f11, f1 -> f1, h1 -> h1, g11 -> g11,
           g1 -> g1, k1 -> k1, mm1 -> mm1, p1 -> p1, p11 -> p11,
           d1 -> d1, e -> e, r -> r, fm11 -> fm11, fm1 -> fm1,
          hm1 -> hm1, gm11 -> gm11, gm1 -> gm1, km1 -> km1,
          rm -> rm} &[
       soln = Quiet@
         Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1, mm1, p1,
            p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
           rm}, {species10, species20, species30}, tmax]]]}],
   Evaluate[{Im[
      eigen /. {n1 -> #[[1]], y -> #[[2]], m -> #[[3]], b1 -> b1,
          a11 -> a11, f11 -> f11, f1 -> f1, h1 -> h1, g11 -> g11,
          g1 -> g1, k1 -> k1, mm1 -> mm1, p1 -> p1, p11 -> p11,
          d1 -> d1, e -> e, r -> r, fm11 -> fm11, fm1 -> fm1,
          hm1 -> hm1, gm11 -> gm11, gm1 -> gm1, km1 -> km1,
          rm -> rm} &[
       soln =
        Quiet@Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1,
           mm1, p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
           rm}, {species10, species20, species30}, tmax]]]}], {t, 0,
    Min[tmax, Min[#[[1, 1, 2]] & /@ soln]]},
   AxesLabel ->
    TraditionalForm /@ {t, {Style[e1, col1], Style[e2, col2],
       Style[e3, col3]}}, PlotRange -> All, AxesOrigin -> {0, 0},
   PlotStyle -> {col1, col2, col3}, ImageSize -> {500, 500},
   ImagePadding -> {{40, 10}, {10, 25}}]], {{b1, 1, "b1"}, 0, 2, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{a11, 1, "a11"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{f11, 1, "f11"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{f1, 1, "f1"}, 0,
  1, .01, ImageSize -> Tiny, Appearance -> "Labeled"}, {{h1, 1, "h1"},
   0, 1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{g11, 1, "g11"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{p1, 1, "p1"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{p11, 1, "p11"}, 0.1, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{d1, 1, "d1"}, 0,
  1, .01, ImageSize -> Tiny, Appearance -> "Labeled"}, {{g1, 1, "g1"},
   0, 1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{k1, 1, "k1"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{mm1, 1, "mm1"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{fm11, 1, "fm11"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{fm1, 1, "fm1"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{hm1, 1, "hm1"}, 0.1, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{gm1, 1, "gm1"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{gm11, 1, "gm11"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{km1, 1, "km1"}, 0,
  1, .01, ImageSize -> Tiny, Appearance -> "Labeled"}, {{e, 1, "e"},
  0, 1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{r, 1, "r"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{rm, 1, "rm"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance ->
   "Labeled"}, Delimiter, "initial populations", {{species10, 1,
   "species10"}, 0, 10,
  ImageSize -> Tiny}, {{species20, 1, "species20"}, 0, 10,
  ImageSize -> Tiny}, {{species30, 1, "species30"}, 0, 10,
  ImageSize -> Tiny}, {{t, 1, "time"}, 0, 10, ImageSize -> Tiny},
SaveDefinitions -> True, ControlPlacement -> Left]
POSTED BY: Bene Bachelot
I'm sorry I did not realize there could be some corruption. Here is the code I have been trying to use to manipulate the eigenvalues:
 Manipulate[
  Module[{soln, col1 = RGBColor[1, .47, 0],
    col2 = ColorData["HTML", "SlateBlue"],
    col3 = ColorData["HTML", "Black"]},
   Plot[Evaluate[{Re[
       eigen /. {#[[1]], #[[2]], #[[3]], b1, a11, f11, f1, h1, g11, g1,
            k1, mm1, p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
            rm} &[soln =
         Quiet@Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1,
           mm1, p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
           rm}, {species10, species20, species30}, tmax]]]}],
   Evaluate[{Im[
      eigen /. {#[[1]], #[[2]], #[[3]], b1, a11, f11, f1, h1, g11, g1,
           k1, mm1, p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
           rm} &[soln =
        Quiet@Benesystem[{b1, a11, f11, f1, h1, g11, g1, k1,
           mm1, p1, p11, d1, e, r, fm11, fm1, hm1, gm11, gm1, km1,
           rm}, {species10, species20, species30}, tmax]]]}], {t, 0,
    Min[tmax, Min[#[[1, 1, 2]] & /@ soln]]},
   AxesLabel ->
    TraditionalForm /@ {t, {Style[e1, col1], Style[e2, col2],
       Style[e3, col3]}}, PlotRange -> All, AxesOrigin -> {0, 0},
   PlotStyle -> {col1, col2, col3}, ImageSize -> {500, 500},
   ImagePadding -> {{40, 10}, {10, 25}}]], {{b1, 1, "b1"}, 0, 2, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{a11, 1, "a11"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{f11, 1, "f11"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{f1, 1, "f1"}, 0,
  1, .01, ImageSize -> Tiny, Appearance -> "Labeled"}, {{h1, 1, "h1"},
   0, 1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{g11, 1, "g11"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{p1, 1, "p1"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{p11, 1, "p11"}, 0.1, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{d1, 1, "d1"}, 0,
  1, .01, ImageSize -> Tiny, Appearance -> "Labeled"}, {{g1, 1, "g1"},
   0, 1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{k1, 1, "k1"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{mm1, 1, "mm1"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{fm11, 1, "fm11"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{fm1, 1, "fm1"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{hm1, 1, "hm1"}, 0.1, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{gm1, 1, "gm1"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{gm11, 1, "gm11"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{km1, 1, "km1"}, 0,
  1, .01, ImageSize -> Tiny, Appearance -> "Labeled"}, {{e, 1, "e"},
  0, 1, .01, ImageSize -> Tiny,
  Appearance -> "Labeled"}, {{r, 1, "r"}, 0, 1, .01,
  ImageSize -> Tiny, Appearance -> "Labeled"}, {{rm, 1, "rm"}, 0,
  1, .01, ImageSize -> Tiny,
  Appearance ->
   "Labeled"}, Delimiter, "initial populations", {{species10, 1,
   "species10"}, 0, 10,
  ImageSize -> Tiny}, {{species20, 1, "species20"}, 0, 10,
  ImageSize -> Tiny}, {{species30, 1, "species30"}, 0, 10,
  ImageSize -> Tiny}, {{t, 1, "time"}, 0, 10, ImageSize -> Tiny},
SaveDefinitions -> True, ControlPlacement -> Left]
POSTED BY: Bene Bachelot
Posted 10 years ago
Hi Bene,

The first thing that stands out to me is that you are using ReplaceAll without a a list of rules.
eigen /. {1, 2, 3}
The list needs to contain rules like
{a -> 1, b -> 2, c -> 3}
POSTED BY: Michael Hale
Copying and pasting Mathematica code into a text box can corrupt the code.  It would be better to copy your code into a "spikey" box.
POSTED BY: Frank Kampas
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