Birth of canard cycles

DOI10.3934/dcdss.2009.2.723zbMath1186.34080OpenAlexW2077367792MaRDI QIDQ1045961

Robert Roussarie, Freddy Dumortier

Publication date: 21 December 2009

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

Full work available at URL: https://doi.org/10.3934/dcdss.2009.2.723

zbMATH Keywords

singular perturbationHopf bifurcationturning pointLiénard equationslow-fast systemcanard cycle

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) 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) Singular perturbations for ordinary differential equations (34E15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Relaxation oscillations for ordinary differential equations (34C26) Canard solutions to ordinary differential equations (34E17)

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