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Discretized Fast–Slow Systems with Canards in Two Dimensions.
- Source :
-
Journal of Nonlinear Science . Apr2022, Vol. 32 Issue 2, p1-41. 41p. - Publication Year :
- 2022
-
Abstract
- We study the problem of preservation of maximal canards for time discretized fast–slow systems with canard fold points. In order to ensure such preservation, certain favorable structure-preserving properties of the discretization scheme are required. Conventional schemes do not possess such properties. We perform a detailed analysis for an unconventional discretization scheme due to Kahan. The analysis uses the blow-up method to deal with the loss of normal hyperbolicity at the canard point. We show that the structure-preserving properties of the Kahan discretization for quadratic vector fields imply a similar result as in continuous time, guaranteeing the occurrence of maximal canards between attracting and repelling slow manifolds upon variation of a bifurcation parameter. The proof is based on a Melnikov computation along an invariant separating curve, which organizes the dynamics of the map similarly to the ODE problem. [ABSTRACT FROM AUTHOR]
- Subjects :
- *QUADRATIC fields
*INVARIANT manifolds
Subjects
Details
- Language :
- English
- ISSN :
- 09388974
- Volume :
- 32
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Nonlinear Science
- Publication Type :
- Academic Journal
- Accession number :
- 154582065
- Full Text :
- https://doi.org/10.1007/s00332-021-09778-2