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.