I have a system of differential equations with two discrete variables (var1 and var2) that can be either 0 or 1. I'm trying to obtain a numerical solution with NDSolve for such system. I want to be able to manipulate those discrete variables independently, i.e, make var1 = 0 at t = 3, and become 1 at t = 6, and back to 0 at t =9, and so on. I also want to make var2 = 0 at t = 4, and become 1 at t = 8, and back to 0 at t = 12, and so on.
My initial attempt looks like this
parameters = {..., periodvar1=3, periodvar2=4,...}
solution = NDsolve[eqx,eqy,eqz,
WhenEvent[Mod[t,periodvar1], {var1[t] -> 0}],
WhenEvent[Mod[t,periodvar2], {var1[t] -> 1}],
WhenEvent[Mod[t,periodvar1], {var2[t] -> 0}],
WhenEvent[Mod[t,periodvar2], {var2[t] -> 1}],
x[0] = 1, y[0] = 1, z[0] =1, var1[0] =1, var2[0] =0} /.parameters,
{x[t], y[t],z[t]}, {t,0,100},
DiscreteVariables -> {var1,var2}];
I figured out that this approach keeps var1 = 1 and var2 = 1 for every t (It seems like the last WhenEvent prevails over the previous). I tried also something like:
WhenEvent[{Mod[t,periodvar1],var1==1}, {var1[t] -> 0}],
WhenEvent[{Mod[t,periodvar2],var1==0}, {var1[t] -> 1}],
WhenEvent[{Mod[t,periodvar1],var2==1}, {var2[t] -> 0}],
WhenEvent[{Mod[t,periodvar2],var2==0}, {var2[t] -> 1}],
And finally:
WhenEvent[{Sin[t*pi/periodvar1] >= 0, Sin'[t*pi/periodvar1] > 0}, var1[t] -> 1],
WhenEvent[{Sin[t*pi/periodvar1] <= 0, Sin'[t*pi/periodvar1] < 0}, var2[t] -> 0],
But the result were either fixed var1 or error messages. Is there a clean way to do this? (To make the point clear, my example started with two variables but I aim to progressively add more variables so it should be extendable).
