an issue for time-depent lags dde of a common model in laser about delaydiffeq.jl

[ChrisRackauckas]

Transferred from docs to DelayDiffEq.jl. @devmotion do you think it might be a weird instability issue related to #67 ?

[devmotion]

Hmm.... It seems the provided example errors since S(t)S(t-tau_ext) becomes negative and hence it's not possible to compute the square root of this term anymore. I guess that's also the reason for the lines you commented out (BTW they are not correct since you try to write complex values to a vector of real numbers)?

First of all, it would be interesting to see your MATLAB implementation, if that's possible. Did you consider possibly negative values of S(t)S(t-tau_ext) therein (e.g. by specifying that S should be non-negative)? Or did you just constrain the step size?

Actually, a bit more than one year ago I worked with a DDE that was also not defined for negative values. You can find a Julia implementation of it here, and you can also have a look at simulations with different solvers. As you can see in the Julia implementation, I set the derivatives of variables that should be non-negative to max(0, dxdt), following Shampine's advice. In my case, this implementation together with a suitable algorithm such as Rodas5 was sufficient to be able to compute simulations of my model reliably. However, you might want to have a look at isoutofdomain and the PositiveDomain callback, which are explained in the documentation. Another approach (which might be a bit more elegant) could be to enforce the positivity of S by considering the dynamics of a new variable T = f(S) instead of the dynamics of S, where f is a bijective function and T is unconstrained, contrary to S.

[PeterXiaoGuo]

Thanks for your reply! @devmotion
Actually, S(t) has a physical meaning - it's photon density. Therefore, it cannot be negative.
the lines you commented out is an naive attempt to let program runs and it fails.
I will try your advice and update how 's it going in Julia.

Thanks,
Peter