Singular perturbations and vanishing passage through a turning point

DOI10.1016/j.jde.2009.11.009zbMath1277.34081OpenAlexW2090374067MaRDI QIDQ963716

Freddy Dumortier, Peter De Maesschalck

Publication date: 13 April 2010

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.11.009

zbMATH Keywords

singular perturbationsblow-upturning pointcanardsslow-fast cycle

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Singular perturbations for ordinary differential equations (34E15) Relaxation oscillations for ordinary differential equations (34C26) Canard solutions to ordinary differential equations (34E17)

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Cites Work

• Unnamed Item
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• Quadratic Models for Generic Local 3-Parameter Bifurcations on the Plane
• Desingularization of nilpotent singularities in families of planar vector fields
• Canard cycles and center manifolds
• Partially hyperbolic fixed points with constraints
• Multiple canard cycles in generalized Liénard equations

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