Structural Stability in 4-Dimensional Canards

作     者：Shuya Kanagawa Kiyoyuki Tchizawa Shuya Kanagawa;Kiyoyuki Tchizawa

作者机构：Deparatment of Mathematics Tokyo City University Tokyo Japan Deparatment of Mathematics Tokyo Gakugei University Tokyo Japan Institute of Administration Engineering Ltd. Sotokanda Tokyo Japan 

出 版 物：《Advances in Pure Mathematics》 (理论数学进展（英文）)

年 卷 期：2022年第12卷第11期

页      面：600-613页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

摘      要：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.