Discretized Fast-Slow Systems near Transcritical Singularities
Dynamical Systems
2019-07-16 v1
Abstract
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.
Cite
@article{arxiv.1806.06561,
title = {Discretized Fast-Slow Systems near Transcritical Singularities},
author = {Maximilian Engel and Christian Kuehn},
journal= {arXiv preprint arXiv:1806.06561},
year = {2019}
}