Sounds like the question is resolved. Will paste the comments here:
Looks like you are using a much earlier version of MATLAB. I wonder whether it would help to see if where is any shipping demo using that variable displacement pump. In R2020a shipping demo, there is one example with that pump and a reservior, which, if available in your version, can be a good reference.
I also believe that "displacement" quantity refers to the ratio between flowrate and angular velocity, instead of the instaneous location of the pistons, so you won't see any reciprocal motion.
Thanks for your answer, i couldn't adapt an exemple to my need but i added a reservoir with ckeck valves at the entry of my pump and it worked (even though this don't represent a closed loop circuit anymore).
After doing some research, i think the better solution tu resolve the solver problem " pressure fell bellow absolute zero " would be to upgrade my version of matlab, as newer version can continue the simulation after this problem, but not the 2013 version.