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Canards Flying on Bifurcation
Deparatment of Mathematics, Tokyo City University, Tokyo, Japan
Institute of Administration Engineering, Ltd., Tokyo, Japan
- 1 Deparatment of Mathematics, Tokyo City University, Tokyo, Japan
- 2 Institute of Administration Engineering, Ltd., Tokyo, Japan
Advances in Pure Mathematics·Volume 13 (2023)·Pages 412–424·Published 25 June 2023·DOI10.4236/apm.2023.136026
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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.
KeywordsCanard SolutionSlow-Fast SystemNonstandard AnalysisHilbert’s 16th ProblemBrownian MotionStochastic Differential Equation
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