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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?

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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.

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  • $\begingroup$ My solutions are quite complex to check the discontinuities but I think it may due to the deviation from the harmonic oscillator. Thank you. $\endgroup$ – user199009 Apr 22 at 10:11
  • $\begingroup$ @TheDreamer - What is the system? $\endgroup$ – Anders Sandberg Apr 22 at 15:40

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