If somebody declares himself Julius Cesar, Jesus Christ, Napoleon, etc. he may well end up in a madhouse. However, if he declares that TRIZ and catastrophe theory have something in common, he gets published in the TRIZ-journal ! The less understandable (for the common people) a delirium is, the higher chances that it will be related to scientific papers !
Take, for example, Bushuev's "work" on modelling TRIZ by "cusp catastrophe". The basis for such a "modelling" is the fact that depending on parameters a and b, the function
V(z) = 0.25 z4 - 0.5 az2 - bz
has either one local minimum, or two local minima. Bushuev recognized "evolution" here: with parameters change, we have transition from mono-minimum to bi-minimum ! Great ! Next step: in TRIZ there is also transition from mono-system to bi-system. Hence, due to Bushuev's logic, this transition can be modelled by transition from mono-minimum to bi-minimum, if one identifies minimums with systems (or at least with their stable states) !
Well, there are many other mono-to-bi transitions in the world. The most famous one is change in the number of objects that a drunk observes. Depending on the degree of his alcoholic intoxication, he initially sees one object, then two objects, then many objects ! Why would not model technical contradictions (and TRIZ on the whole) with the help of this phenomenon ? It has clear advantages over "cusp catastrophe": it exibits complete mono-bi-poly transition, whereas "cusp catastrophe" exibits only mono-to-bi transition. Moreover, the alcoholic intoxication model points to a missed stage in the TRIZ law of evolution. Namely, transition from poly to nothing: if drunk takes in more alcohol after observing multiple images, he eventually fell unconcious and starts observing nothing.