See also the section on tolerances for more information about this. If they are too long - particularly if they enter a limit cycle - they will be stopped, and also if they approach equilibrium points. Note that trajectories can also be terminated for other reasons. For example, if PortraitBoundsTolerance is 1.5 and the area is the square. PortraitBoundsTolerance is a multiplier that increases the size of the area of that trajectories are allowed to travel in without having an effect on the displayed area. However, sometimes trajectories could leave the area and then come back after a while if integration would be continued. If a trajectory leaves the predefined area the integrator will stop that trajectory at that point. If the aspect ratio of the plot is one, there are exactly PortraitDensity number of cells along each direction. PortraitDensity is the number of cells along the shortest end of the plot. When all cells are occupied the algorithm is done. Trajectories are added to the phase portrait one by one when the next trajectory is selected it cannot start in an occupied cell. When a trajectory passes through a cell it is marked as "occupied". It starts by dividing up the area into cells, which are marked "empty". To understand what exactly PortraitDensity is, it helps to know how the algorithm that picks trajectories works. A lower number gives a more sparse phase portrait. PortraitDensity determines the density of the phase portrait. It can also be given any options that can be given to ParametricPlot, such as PlotTheme or Epilog. PhasePortrait` can be controlled through several options that are listed here below.
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