TITLE:
Canards Flying on Bifurcation
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.13 No.6,
June
29,
2023
ABSTRACT: There exists a property “structural stability” for “4-dimensional canards” which is a singular-limit solution in a slow-fast system with a bifurcation parameter. It means that the system includes the possibility to have some critical values on the bifurcation parameter. Corresponding to these values, the pseudo-singular point, which is a singular point in the time-scaled-reduced system should be changed to another one. Then, the canards may fly to another pseudo-singular point, if possible. Can the canards fly? The structural stability gives the possibility for the canards flying. The precise reasons why happen are described in this paper.