From canards of folded singularities to torus canards in a forced van der Pol equation

DOI10.1007/s00332-015-9279-0zbMath1346.34042arXiv1504.03970OpenAlexW1688235387MaRDI QIDQ266425

F. Blanchet-Sadri, M. Dambrine

Publication date: 13 April 2016

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.03970

zbMATH Keywords

normal formcanardsfolded singularitiesgeometric desingularisationmixed-mode oscillationtorus bifurcationtorus canards

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Neural biology (92C20) Geometric methods in ordinary differential equations (34A26) Bifurcation theory for ordinary differential equations (34C23) Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Averaging method for ordinary differential equations (34C29) Invariant manifolds for ordinary differential equations (34C45) Singular perturbations for ordinary differential equations (34E15) Multiple scale methods for ordinary differential equations (34E13) Nonautonomous smooth dynamical systems (37C60) Canard solutions to ordinary differential equations (34E17)

Related Items

Multi-mode attractors and spatio-temporal canards ⋮ A survey on the blow-up method for fast-slow systems ⋮ Generalized Play Hysteresis Operators in Limits of Fast-Slow Systems ⋮ Generic torus canards ⋮ Global phase portraits of the generalized van der Pol systems ⋮ Geometric blow-up for folded limit cycle manifolds in three time-scale systems ⋮ Gevrey solutions of singularly perturbed differential equations, an extension to the non-autonomous case

Uses Software

• AUTO
• AUTO-07P

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