Discretized fast–slow systems near pitchfork singularities
| Autor: | Luca Arcidiacono, Maximilian Engel, Christian Kuehn |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Algebra and Number Theory
34E15 37M99 37G10 34C45 39A99 Discretization Applied Mathematics Mathematical analysis Dynamical Systems (math.DS) Singular point of a curve Dynamical system Euler method symbols.namesake Singularity Ordinary differential equation Slow manifold FOS: Mathematics symbols Gravitational singularity Mathematics - Dynamical Systems Analysis Mathematics |
| Zdroj: | Journal of Difference Equations and Applications. 25:1024-1051 |
| ISSN: | 1563-5120 1023-6198 |
| Popis: | Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking trajectories in the vicinity of the singularity we show, how the slow manifold extends beyond the singular point and give an estimate on the contraction rate of a transition mapping. The proof relies on the blow-up method suitably adapted to the discrete setting where a key technical contribution are precise estimates for a cubic map in the central rescaling chart. 29 pages, 7 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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