Bifurcation on 4-dimensional Canards with Hyper Catastrophe

In 4-dimensional slow-fast system, under the condition of ”symmetry”, there exists ”structural stability”. It is, however, of one parameter for the slow vector. On other parameters for all slow/fast vectors, it is not yet discussed still now as it is very complicated geometrical structure. In the ”Hyper catastrophe on 4-dimensional canards”, it is confirmed due to the existence of ”bifurcation”, because ”catastrophe” is a bifurcation problem itself. In the beginning of catastrophe theory, the word ”structural stability” is used for the original differential equations and not be used for the multi variable functions. In the slow-fast system having canards, what kinds of structure are there? It is used for the parameter, which depends on the existence of canards. Through this paper, it will become clear.