Canard-cycle transition at a fast-fast passage through a jump point

DOI10.1016/j.crma.2013.09.002zbMath1287.34044OpenAlexW1995219546MaRDI QIDQ2438557

Freddy Dumortier, Robert Roussarie, Peter De Maesschalck

Publication date: 5 March 2014

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2013.09.002

zbMATH Keywords

breaking mechanismfast-fast passagetransitory canard cycles

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Singular perturbations for ordinary differential equations (34E15) Canard solutions to ordinary differential equations (34E17)

Related Items (8)

Spike-adding in parabolic bursters: the role of folded-saddle canards ⋮ Relaxation oscillations in a slow-fast predator-prey model with weak Allee effect and Holling-IV functional response ⋮ Canards, heteroclinic and homoclinic orbits for a slow-fast predator-prey model of generalized Holling type III ⋮ Canard cycle transition at a slow-fast passage through a jump point ⋮ Relaxation oscillations and canards of a regulated two-gene model ⋮ Parabolic bursting, spike-adding, dips and slices in a minimal model ⋮ Canards and homoclinic orbits in a slow-fast modified May-Holling-Tanner predator-prey model with weak multiple allee effect ⋮ Planar canards with transcritical intersections

Cites Work

• Cyclicity of common slow-fast cycles
• Birth of canard cycles
• Slow divergence integral and balanced canard solutions
• Canard cycle transition at a slow-fast passage through a jump point
• Multiple canard cycles in generalized Liénard equations
• Relaxation oscillation and canard explosion

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