Conjecture concerning various behavioral scenarios of the mystic:

1. Make a phase portrait of purgation and from it find the region of the portrait where the system is attracted to the state of mystical union. If the attractor is Liapunov stable, this may mean that the experiencer becomes an avatar or arhat, remaining within the basin of attraction in an orbit near the attractor or fixed point. Then, determine how certain variables of the model (and the relationship between these variables) contribute to the stability of the fixed point or attractor. One can then make an analysis to determine the range of the set of variables that would produce an avatar or arhat. Phase portraits that show the mystic's behavior traversing regions outside the basin of attraction would be of interest to comparative religion scholars, anthropologists, religiously oriented social workers, some psychiatrists, etc. - particularly if a limit cycle or unstable spiral exists in the region outside of the basin of attraction or if the fixed point is unstable. Behavioral scenarios that traverse regions outside the basin of attraction may produce the behavioral category of saint or bodhisattvas or other behavioral scenarios that are problematic and difficult to categorize. These phase portrait analyses could give insights into the incredible phenomena of avatars or arhats. Explaining in detail the other more complex categories with such an analysis will obviously be extremely difficult.
2. Examine the conjecture that the removal of knots during Purgation has the effect of a catalyst, leading to a phase transition and the emergence of the self organized state of mystical union.

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