Side-comparison for transition maps in multi-layer canard problems

DOI10.1134/s1560354723040159zbMath1524.34139OpenAlexW4387828184MaRDI QIDQ6069642

Peter De Maesschalck, Robert Roussarie, Freddy Dumortier

Publication date: 14 November 2023

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354723040159

zbMATH Keywords

connection diagramequations for limit cyclesmulti-layer canard cyclesorientation of \(SF\) and \(FS\) passagesside-comparison at a canard connection

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Singular perturbations of ordinary differential equations (34D15) Singular perturbations for ordinary differential equations (34E15) Canard solutions to ordinary differential equations (34E17)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multiple time scale dynamics
• Cyclicity of common slow-fast cycles
• Composite asymptotic expansions
• Chasse au canard
• Canard cycles of finite codimension with two breaking parameters
• Canard cycles with two breaking parameters
• Canard cycle transition at a slow-fast passage through a jump point
• Multi-layer canard cycles and translated power functions
• Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
• Extending slow manifolds near transcritical and pitchfork singularities
• Mixed-Mode Oscillations with Multiple Time Scales
• Overstability: towards a global study
• Canard cycles and center manifolds
• Canard Cycles
• Geometric Singular Perturbation Theory Beyond the Standard Form

This page was built for publication: Side-comparison for transition maps in multi-layer canard problems