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]
