Manipulate[solution[t_] = NDSolve[{
Derivative[1][w][t] == - k1 S w[t] + k2 x[t] -
k7 H w[t] + k8 y[t],
Derivative[1][x][t] == - k2 x[t] + k1 S w[t] - k3 H x[t] +
k4 z[t],
Derivative[1][y][t] == -k8 y[t] + k7 H w[t] - k5 S y[t] +
k6 z[t],
Derivative[1][z][t] == - k4 z[t] + k3 H x[t] - k6 z[t] +
k5 S y[t], w[0] == 1, x[0] == 0, y[0] == 0,
z[0] == 0}, {w [t],
x [t], y [t], z [t]}, {t, 0, 10}][[1, All, 2]];
Plot[solution[t], {t, 0, 10}], {{k1, 1}, 0.01, 5,
Appearance -> "Labeled"}
, {{k2, 1}, 0.01, 5, Appearance -> "Labeled"}
, {{k3, 1}, 0.01, 5, Appearance -> "Labeled"}
, {{k4, 1}, 0.01, 5, Appearance -> "Labeled"} , {{k5, 1}, 0.01, 5,
Appearance -> "Labeled"} , {{k6, 1}, 0.01, 5,
Appearance -> "Labeled"} , {{k7, 1}, 0.01, 5,
Appearance -> "Labeled"} , {{k8, 1}, 0.01, 5,
Appearance -> "Labeled"} , {{H, 1}, 0.1, 5,
Appearance -> "Labeled"}, {{S, 1}, 0.01, 5,
Appearance -> "Labeled"} ,
TrackedSymbols :> {k1, k2, k3, k4, k5, k6, k7, k8, H, S}]
!(*SuperscriptBox["w", "[Prime]", MultilineFunction->None])[t] == - k1 S w[t] + k2 x[t] - k7 H w[t] + k8 y[t], !(*SuperscriptBox["x", "[Prime]", MultilineFunction->None])[t] == - k2 x[t] + k1 S w[t] - k3 H x[t] + k4 z[t], !(*SuperscriptBox["y", "[Prime]", MultilineFunction->None])[t] == -k8 y[t] + k7 H w[t] - k5 S y[t] + k6 z[t], !(*SuperscriptBox["z", "[Prime]", MultilineFunction->None])[t] == - k4 z[t] + k3 H x[t] - k6 z[t] + k5 S y[t], w[0] == 1, x[0] == 0, y[0] == 0, z[0] == 0}, {w [t], x [t], y [t], z [t]}, {t, 0, 10}][[1, All, 2]]; Plot[solution[t], {t, 0, 10}], {{k1, 1}, 0.01, 5, Appearance -> "Labeled"} , {{k2, 1}, 0.01, 5, Appearance -> "Labeled"} , {{k3, 1}, 0.01, 5, Appearance -> "Labeled"} , {{k4, 1}, 0.01, 5, Appearance -> "Labeled"} , {{k5, 1}, 0.01, 5, Appearance -> "Labeled"} , {{k6, 1}, 0.01, 5, Appearance -> "Labeled"} , {{k7, 1}, 0.01, 5, Appearance -> "Labeled"} , {{k8, 1}, 0.01, 5, Appearance -> "Labeled"} , {{H, 1}, 0.1, 5, Appearance -> "Labeled"}, {{S, 1}, 0.01, 5, Appearance -> "Labeled"} , TrackedSymbols :> {k1, k2, k3, k4, k5, k6, k7, k8, H, S}]
