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Discovering the potential of canards flying in 4-dimensional slow-fast system with one bifurcation parameter, the key notion “symmetry” plays an important role. It is composed of one parameter on slow vector field. Introducing parameters to all slow/fast vectors, it seemed to be no way to explore for another potential, because the geometrical structure is quite different from the system with one parameter. Even in this system, it is shown “symmetry” is also useful to obtain another potential. We consider the slow-fast system having “Brownian motion” in order to confirm the rigidity for the bifurcation structure. It looks like to be a much complex state as the existence of ò in the slow-fast system and having Brownian motion. We overcome the difficulty, since the difference equation on the small time interval adopts the standard differential equation. Under some condition about the “convolution”, it is possible to overcome. Furthermore, introducing the small interval to the extended Wiener process, it becomes to analyze exactly. These small intervals are defined on the “hyper finite time line” by using the finite number N in the sense of nonstandard. As ò and those intervals are linked to use  the simulation should be done well.

canards flying, 4-dimensional slow-fast system, hyper catastrophe.