Can we consider the field of futures probabilities as a chaotic system ?

We illustrate the field of futures probabilities using the concept of the ?cone of plausibility?:

Suppose that for any time value tn in this projected cone we had a value y1 and a value y2 to define the upper and the lower limits of plausibility ? or extremum of the bidimensional cone slice for the time value tn ? see the graph:

Also, we can define a mean for each value of time tn:
M = (y1+y2)/2 
Which would expressed on the graphs by the default vector of time.

  1. Having defined a bounded space, could we consider  the field of future probabilities ? included between y1 and y2 in the cone of plausibility at tn and observable from t0 ? as a chaotic system ?
  2. If it can be considered as so, would it be a linear or a nonlinear system ?
  3. If it can be considered as so, could we call M for the time value tn an attractor ? A global attractor ? Something else ?
  4. Finally, if it can be considered as so and if you had to express your mathematician's point of view, would such a system have any interest, be practical, or useful ?
Thank you for your time. I?ll ask you kindly to include sources for your references.
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  • 0. y_1 and y_2 are not really well defined. The cone is a didactic representation to explain a concept, but there is no way to define a boundary for the possibilities or the 'extremum' of all possibilities. 1. Barring my previous comment, you could choose to model it as such. Modeling is always a choice, I'm afraid. 2. You choose. 3. Depends on the equations we end up positing. 4. I fear there are too many things undefined. The cone works conceptually but not mathematically.

  • Please consider that y1 and y2 are defined as working extremums through a non classical logical system but it cannot be disclosed here. Would it change something ? If i understand correctly, modeling this would produce a totally abstract system. Exploring this part of mathematic for a potential application was necessary before continuing my work. Is there a mathematical working consensus to represent "the futur field of possibilities" ? If yes, is it linear or nonlinear ?