# Is it possible to have discontinuities in the phase portrait of a dynamical system? If yes what does it really mean?

I've been using Mathematica to draw the phase portrait of a system and I got some jumps along the trajectory. I have a deviation term which might be the reason of this but is it possible to have them or I'm doing something wrong?

Phase portraits can't be discontinuous unless the dynamics is discontinuous, since each point of the phase space corresponds to a state. So if the dynamics is expressed through a differential equation there must at least be continuity. Note that trajectories in this case only have to be $$C^0$$ continuous, the derivatives might be discontinuous producing corners and other oddities.