Detectable canard cycles with singular slow dynamics of any order at the turning point

DOI10.3934/DCDS.2011.29.109zbMath1235.34170OpenAlexW2322786755MaRDI QIDQ628760

Freddy Dumortier, Peter De Maesschalck

Publication date: 7 March 2011

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2011.29.109

zbMATH Keywords

singular perturbationsturning pointblow upslow-fast cyclecanardgeneralized Liénard equation

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

Related Items (10)

Box dimension and cyclicity of Canard cycles ⋮ Limit cycles in slow-fast codimension 3 saddle and elliptic bifurcations ⋮ Regular and slow-fast codimension 4 saddle-node bifurcations ⋮ Slow-fast Bogdanov-Takens bifurcations ⋮ Well adapted normal linearization in singular perturbation problems ⋮ Primary birth of canard cycles in slow-fast codimension 3 elliptic bifurcations ⋮ Quartic Liénard equations with linear damping ⋮ Cyclicity of the origin in slow-fast codimension 3 saddle and elliptic bifurcations ⋮ Unnamed Item ⋮ Asymptotic expansions for a degenerate canard explosion

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