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Structural Stability in 4-Dimensional Canards
Deparatment of Mathematics, Tokyo City University, Tokyo, Japan
Deparatment of Mathematics, Tokyo Gakugei University, Tokyo, Japan
Institute of Administration Engineering, Ltd., Sotokanda, Tokyo, Japan
- 1 Deparatment of Mathematics, Tokyo City University, Tokyo, Japan
- 2 Deparatment of Mathematics, Tokyo Gakugei University, Tokyo, Japan
- 3 Institute of Administration Engineering, Ltd., Sotokanda, Tokyo, Japan
Advances in Pure Mathematics·Volume 12 (2022)·Pages 600–613·Published 2 November 2022·DOI10.4236/apm.2022.1211046
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Abstract
Let us consider higher dimensional canards in a sow-fast system R 2+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.
KeywordsCanard SolutionSlow-Fast SystemNonstandard AnalysisHilbert’s 16th ProblemBrownian MotionStochastic Differential Equation
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