Blanchard-Kahn conditions and explosive dynamics


as far as I understand, Blanchard-Kahn conditions are conditions ensuring that there is local determinacy, meaning that there is only one transitional equilibrium path. I read that Blanchard-Kahn conditions can only be used when the series do not explode, that this is a requirement.
Therefore, how does Dynare exclude the case in which series explode before checking for the Blanchard-Kahn conditions ? Is this simply by adding a transversality condition ? How is this coded in Matlab files ?

In addition, I met a case in which Blanchard-Kahn conditions are satisfied, the model runs well in Dynare, but when I simulate the time path of my variables (not IRF but time paths when there are random shocks in each period), there are explosive (but the IRFs are not).
So should I deduce that Blanchard Kahn conditions only ensure that endogenous variables go back to their steady state values after one shock but not that time paths with shocks in each period are not explosive ? I understand that these are distinct concepts, because time paths with shocks in each period will not converge to steady state in any case, by definition, but they can either be stable or explosive though.

Thanks a lot for any clarification

I think you are confusing things here. You cannot solve a model where the BK conditions are not satisfied using perturbation techniques. Otherwise the transversality conditions would not be satisfied.
What you describe is a problem with higher-order perturbation techniques. When order>1 without pruningyou might get explosive dynamics. See e.g. [IRFs are NaN)

I am using first-order perturbation techniques but I just realized that I have a unit root, this should be why I get explosive paths.