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Guckenheimaer, J. and Holmes, P. (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. In: Applied Mathematical Sciences, Vol. 42, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo.

has been cited by the following article:

• TITLE: Structural Stability in 4-Dimensional Canards

  AUTHORS: Shuya Kanagawa, Kiyoyuki Tchizawa

  KEYWORDS: Canard Solution, Slow-Fast System, Nonstandard Analysis, Hilbert’s 16th Problem, Brownian Motion, Stochastic Differential Equation

  JOURNAL NAME: Advances in Pure Mathematics, Vol.12 No.11, November 4, 2022

  ABSTRACT: Let us consider higher dimensional canards in a sow-fast system R2+2 with a bifurcation parameter. Then, the slow manifold sometimes shows various aspects due to the bifurcation. Introducing a key notion “symmetry” to the slow-fast system, it becomes clear when the pseudo singular point obtains the structural stability or not. It should be treated with a general case. Then, it will also be given about the sufficient conditions for the existence of the center manifold under being “symmetry”. The higher dimensional canards in the sow-fast system are deeply related to Hilbert’s 16th problem. Furthermore, computer simulations are done for the systems having Brownian motions. As a result, the rigidity for the system is confirmed.