I have fond memories from back in high school (1700's), when "Catastrophe Theory" was the bee's knees, and was going to explain everything unstable. I remember reading a Scientific American article on CT and thinking that it was very cool, but had that smell of a fast one being pulled somewhere. Turns out I was more or less spot on.
Later in college, I encountered a paper where someone had taken the chemistry of some creature and created an arrow diagram of how every molecule was turned into other molecules. Then they made a big matrix and took eigenstates. Sudden jumps in behaviour occurred when the system switched from one eigenstate to another. A bit like you discussed, but I recall a storage mechanism like you discussed above.