41 citations · 164 across the 26 of their papers we have counts for
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Symmetries of Ordinary Differential Equations: A Short Introduction
Sebastian Walcher
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary…
Coordinate-independent criteria for Hopf bifurcations
Niclas Kruff, Sebastian Walcher
We discuss the occurrence of Poincaré-Andronov-Hopf bifurcations in parameter dependent ordinary differential equations, with no a priori assumptions on special coordinates. The fi…
A coordinate-independent version of Hoppensteadt's convergence theorem
Christian Lax, Katrin Seliger, Sebastian Walcher
The classical theorems about singular perturbation reduction (due to Tikhonov and Fenichel) are concerned with convergence on a compact time interval (in slow time) as a small para…
Classical quasi-steady state reduction -- A mathematical characterization
Alexandra Goeke, Sebastian Walcher, Eva Zerz
We discuss parameter dependent polynomial ordinary differential equations that model chemical reaction networks. By classical quasi-steady state (QSS) reduction we understand the f…