Select the Basin of Attraction view from the pull down menu at the top right of the display. This view contains a section of the (x,x') plane just like the Phase Space Projection view. The difference here is that you may use the mouse button to mark any point in the plane accessible to the cursor. As happens in some other views, a cross hair marks the point on the screen and the coordinates appear in the lower border. What also happens in this view is that the coordinates of the marked point become the initial conditions for the model.
After clicking the mouse button to mark the point you are curious about, click on Action. The program will plot the orbit projection from the marked point to the attractor which own that point. When the orbit settles down to an attractor, you should be able to recognize it as one of those attractors identified from the Phase Space Projection view. What you will find is that there is no way to predict ahead of time which points in the (x,x') plane are owned by which attractor.