Canard cycles in generic fast-slow systems on the torus

DOI10.1090/S0077-1554-2010-00184-7zbMath1276.34047OpenAlexW2093050306MaRDI QIDQ3086104

I. V. Shchurov

Publication date: 29 March 2011

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0077-1554-2010-00184-7

zbMATH Keywords

dynamical systemfast-slow systemslow curveattracting canard cycle

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Multiple scale methods for ordinary differential equations (34E13) Canard solutions to ordinary differential equations (34E17)

Related Items (4)

Spike-adding in parabolic bursters: the role of folded-saddle canards ⋮ Duck factory on the two-torus: multiple canard cycles without geometric constraints ⋮ Slow-fast torus knots ⋮ Parabolic bursting, spike-adding, dips and slices in a minimal model

Cites Work

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• Ducks on the torus: existence and uniqueness
• The canard unchained or how fast/slow dynamical systems bifurcate
• Geometric singular perturbation theory for ordinary differential equations
• On invariant manifolds in singularly perturbed systems
• Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
• Canard cycles and center manifolds

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