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Extended and Symmetric Loss of Stability for Canards in Planar Fast-Slow Maps.
- Source :
-
SIAM Journal on Applied Dynamical Systems . 2020, Vol. 19 Issue 4, p2530-2566. 37p. - Publication Year :
- 2020
-
Abstract
- We study fast-slow maps obtained by discretization of planar fast-slow systems in continuous time. We focus on describing the so-called delayed loss of stability induced by the slow passage through a singularity in fast-slow systems. This delayed loss of stability can be related to the presence of canard solutions. Here we consider three types of singularities: transcritical, pitchfork, and fold. First, we show that under an explicit Runge--Kutta discretization the delay in loss of stability, due to slow passage through a transcritical or a pitchfork singularity, can be arbitrarily long. In contrast, we prove that under a Kahan--Hirota--Kimura discretization scheme, the delayed loss of stability related to all three singularities is completely symmetric in the linearized approximation, in perfect accordance with the continuous-time setting. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CONTINUOUS time systems
Subjects
Details
- Language :
- English
- ISSN :
- 15360040
- Volume :
- 19
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Applied Dynamical Systems
- Publication Type :
- Academic Journal
- Accession number :
- 147865562
- Full Text :
- https://doi.org/10.1137/20M1313611