Abstract:
The paper deals with multi-layer canard cycles, extending the results of [1]. As
a practical tool we introduce the connection diagram of a canard cycle and we show how to
determine it in an easy way. This connection diagram presents in a clear way all available
information that is necessary to formulate the main system of equations used in the study of
the bifurcating limit cycles. In a forthcoming paper we will show that both the type of the layers
and the nature of the connections between the layers play an essential role in determining the
number and the bifurcations of the limit cycles that can be created from a canard cycle.
Keywords:
multi-layer canard cycles, orientation of $SF$ and $FS$ passages, side-comparison at a
canard connection, connection diagram, equations for limit cycles.
Citation:
Peter De Maesschalck, Freddy Dumortier, Robert Roussarie, “Side-Comparison for Transition Maps in Multi-Layer Canard Problems”, Regul. Chaotic Dyn., 28:4-5 (2023), 763–780
\Bibitem{De DumRou23}
\by Peter De Maesschalck, Freddy Dumortier, Robert Roussarie
\paper Side-Comparison for Transition Maps in Multi-Layer Canard Problems
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 4-5
\pages 763--780
\mathnet{http://mi.mathnet.ru/rcd1232}
\crossref{https://doi.org/10.1134/S1560354723040159}
Linking options:
https://www.mathnet.ru/eng/rcd1232
https://www.mathnet.ru/eng/rcd/v28/i4/p763
This publication is cited in the following 1 articles:
Peter De Maesschalck, Freddy Dumortier, Robert Roussarie, “A systematic study of two-dimensional 2-layer canard cycles”, Nonlinearity, 38:5 (2025), 055015
Citation in format AMSBIB
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