The loss of stability or disappearance of a periodic orbit corresponds to a certain bifurcation: the main stability boundaries correspond to bifurcations of codimension 1 (i.e. those that occur in one-parameter families of the general position). For systems on a plane, there are four such stability boundaries, all discovered and described by Leontovich and Andronov. These are also the existence boundaries, i.e. the periodic orbit disappears at the bifurcation moment or immediately after it. Namely, the periodic orbit either
Now all we need to do is knowing how to attribute the dimensions the system determining the bitcoin price has and we can arrive at a model.
No srsly I doubt we can but it's interesting to know how it would be explained if we knew.