Side-Comparison for Transition Maps in Multi-Layer Canard Problems

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 for...

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Bibliographic Details
Published in:Regular & chaotic dynamics 2023, Vol.28 (4-5), p.763-780
Main Authors: Maesschalck, Peter De, Dumortier, Freddy, Roussarie, Robert
Format: Article
Language:English
Subjects:
Bifurcations
Dynamical Systems and Ergodic Theory
Mathematical Physics
Mathematics
Mathematics and Statistics
Mechanics
Multilayers
Physics
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Summary: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.
ISSN:1560-3547
1560-3547
1468-4845
DOI:10.1134/S1560354723040159