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arXiv · 1806.06561

Discretized Fast-Slow Systems near Transcritical Singularities

Maximilian Engel·Christian Kuehn
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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.

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Maximilian Engel, Christian Kuehn. 2018-06-18. Discretized Fast-Slow Systems near Transcritical Singularities. https://doi.org/10.1088/1361-6544%2Fab15c1

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