Discretized fast-slow systems near transcritical singularities
| Autor: | Maximilian Engel, Christian Kuehn |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Discretization
Applied Mathematics 010102 general mathematics Mathematical analysis General Physics and Astronomy Statistical and Nonlinear Physics Dynamical Systems (math.DS) 01 natural sciences 010101 applied mathematics Singularity Transcritical bifurcation Chart FOS: Mathematics Gravitational singularity Mathematics - Dynamical Systems 0101 mathematics Special case 34E15 34E20 37M99 37G10 34C45 39A99 Trajectory (fluid mechanics) Scaling Mathematical Physics Mathematics |
| Zdroj: | Nonlinearity. 32:2365-2391 |
| ISSN: | 1361-6544 0951-7715 |
| Popis: | We extend slow manifolds near a transcritical singularity in a fast-slow system given by the explicit Euler discretization of the corresponding continuous-time normal form. The analysis uses the blow-up method and direct trajectory-based estimates. We prove that the qualitative behaviour is preserved by a time-discretization with sufficiently small step size. This step size is fully quantified relative to the time scale separation. Our proof also yields the continuous-time results as a special case and provides more detailed calculations in the classical (or scaling) chart. |
| Databáze: | OpenAIRE |
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