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Solve numerically a system of 5 ODEs using NDSolve?

Hello all!

I'm trying to solve numerically a system of 5 ODEs using NDSolve[]. The problem is that some of the solutions take negative values, which doesn't make sense from a physical point of view. Is there any way to force these functions to stay non-negative?

I've read about the command WhenEvent[], but I don't know if it can be useful to fix this.

Thank you in advance for any help!

PD: This isn't my mathematical model, which is pretty large, but it might serve as an example:

\[Phi] = 0.08;
a = 0.7;
b = 0.8;
tmax = 200.0;
V0 = 1.0;
U0 = 1.0;
i = 1.0;
sol = NDSolve[{V[0] == V0, U[0] == U0, 
    V'[t] == V[t] - 1/3 V[t]^3 - U[t] + i, 
    U'[t] == \[Phi] (V[t] + a - b U[t])}, V[t], {t, 0, tmax}, 
   DependentVariables -> {V[t], U[t]}, Method -> "Adams"];
Plot[V[t] /. sol, {t, 0, tmax}]
POSTED BY: David G. Aragonés
2 Replies
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The variable U does not change sign:

{solV, solU} = 
  NDSolveValue[{V[0] == V0, U[0] == U0, 
    V'[t] == V[t] - 1/3 V[t]^3 - U[t] + i, 
    U'[t] == \[Phi] (V[t] + a - b U[t])}, {V, U}, {t, 0, tmax}, 
   Method -> "Adams"];
ParametricPlot[{solV[t], solU[t]}, {t, 0, tmax}]
POSTED BY: Gianluca Gorni

Thank you for your answer!

Yes, it's true, U doesn't change sign. I was thinking about the variable V...
POSTED BY: David G. Aragonés
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