Canards Flying on Bifurcation  

作　　者：Shuya Kanagawa Kiyoyuki Tchizawa Shuya Kanagawa;Kiyoyuki Tchizawa(Deparatment of Mathematics, Tokyo City University, Tokyo, Japan;Institute of Administration Engineering, Ltd., Tokyo, Japan)

机构地区：[1]Deparatment of Mathematics, Tokyo City University, Tokyo, Japan [2]Institute of Administration Engineering, Ltd., Tokyo, Japan

出　　处：《Advances in Pure Mathematics》2023年第6期412-424,共13页理论数学进展（英文）

摘　　要：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.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.

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

分 类 号：O17[理学—数学]