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# How to plot and manipulate eigenvalues when changing parameters ?

Posted 11 years ago
 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!BeneHere 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]
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Posted 11 years ago
 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 11 years ago
 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 11 years ago
 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 11 years ago
 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 11 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 11 years ago
 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.