Mathematica Asked by Jerobou on December 19, 2020
I have troubles to understand how to use Manipulate
and ParametricNDSolve
to have modulable parameters inside my models. I checked numerous questions on this forum and couldn’t find one that satisfies my needs (or, more likely, I didn’t understand what to do):
In these examples, the parameters are defined in an equation that isn’t a differential one. I don’t know if it changes anything in my case but its seems to be at the origin of my problem.
Anyway, here is what I did:
First of all, I’ve got this model and these constants:
dEc = p1*Ec[t]*(1 - (Ec[t]/Emax)) - d1*Ec[t] - i1*Ic[t]*Ec[t] - r*Vu[t]*Ec[t];
dIc = i1*Ic[t]*Ec[t] + r*Vu[t]*Ec[t] - u1*Ic[t];
dVp = is[t]*b1*u1*Ic[t] - c1*Vp[t];
dUc = p2*Uc[t]*(1 - (Uc[t]/Umax)) - d2*Uc[t] - i2*Yc[t]*Uc[t] - e*Vp[t]*Uc[t];
dYc = i2*Yc[t]*Uc[t] + e*Vp[t]*Uc[t] - u2*Yc[t];
dVu = is[t]*b2*u2*Yc[t] - c2*Vu[t] + s*Vp[t];
parameters = {Emax -> 10000, Umax -> 10000000, p1 -> 0.6, d1 -> 0.003, d2 -> 0.006, u1 -> 0.33, u2 -> 0.33, c1 -> 10, c2 -> 1, b1 -> 6000, b2 -> 6000, i1 -> 0.0000002, i2 -> 0.0000001, e -> 0.000000001, r -> 0.0000001};
Please note that the parameters p2
and s
are not defined in the parameters
list. It’s because that’s the ones I want to modify using Manipulate
! These parameters are found in equations dUc
and dVu
Then, I do a ParametricNDSolve
on these equations:
dynamicsmodels =
ParametricNDSolve[
Evaluate[{
Ec'[t] == dEc ,
Ic'[t] == dIc ,
Vp'[t] == dVp ,
Uc'[t] == dUc ,
Yc'[t] == dYc ,
Vu'[t] == dVu ,
Ec[0] == 10000, Ic[0] == 0, Vp[0] == 10, Uc[0] == 10000000,
Yc[0] == 0, Vu[0] == 0, is[0] == 0.0005,
WhenEvent[t == 200, is[t] -> 0.0001]
} /. parameters],
{Ec[t], Ic[t], Vp[t], Uc[t], Yc[t], Vu[t]},
{t, 0, 300},
{p2, s},
DiscreteVariables -> {is}[[1]]]
Please note that is[t]
is a variable that evolves in the model following time (see my previous question: Having trouble using WhenEvent with NDSolve).
Then, I do a Manipulate
:
Manipulate[
Plot[
Evaluate[
{
Ec[p2, s][t],
Ic[p2, s][t],
Vp[p2, s][t],
Uc[p2, s][t],
Yc[p2, s][t],
Vu[p2, s][t]
} /. dynamicsmodels
], {t, 0, 300},
PlotRange -> {{0, 300}, {0, 10000}},
PlotStyle -> {Black, Red, Green, Blue, Purple, Orange},
PlotLegends -> {"Ec", "Ic", "Vp", "Uc", "Yc", "Vu"}],
{p2, 1.2, 1.5, Appearance -> "Labeled"},
{s , 1, 100, Appearance -> "Labeled"}
]
I don’t have any error, but no lines either… Am I doing something wrong?
Thanks!
Using ParametricNDSolveValue
:
pndsval = ParametricNDSolveValue[
Evaluate[{Ec'[t] == dEc, Ic'[t] == dIc, Vp'[t] == dVp,
Uc'[t] == dUc, Yc'[t] == dYc, Vu'[t] == dVu, Ec[0] == 10000,
Ic[0] == 0, Vp[0] == 10, Uc[0] == 10000000, Yc[0] == 0,
Vu[0] == 0, is[0] == 0.0005,
WhenEvent[t == 200, is[t] -> 0.0001]} /. parameters], {Ec[t],
Ic[t], Vp[t], Uc[t], Yc[t], Vu[t]}, {t, 0, 300}, {p2, s},
DiscreteVariables -> {is}[[1]]];
Manipulate[Plot[Evaluate[pndsval[p2, s] /. t -> v], {v, 0, 300},
PlotRange -> {{0, 300}, {0, 10000}},
PlotStyle -> {Black, Red, Green, Blue, Purple, Orange},
PlotLegends -> {"Ec", "Ic", "Vp", "Uc", "Yc", "Vu"}], {p2, 1.2, 1.5,
Appearance -> "Labeled"}, {s, 1, 100, Appearance -> "Labeled"}]
Correct answer by kglr on December 19, 2020
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