Folded Saddles and Faux Canards

DOI10.1137/15M1045065zbMath1418.34117MaRDI QIDQ2967815

John Mitry, Martin Wechselberger

Publication date: 2 March 2017

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

fiber bundleMelnikov analysisslow manifoldgeometric singular perturbation theoryfast manifoldfaux canardfolded saddle

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Invariant manifold theory for dynamical systems (37D10) Invariant manifolds for ordinary differential equations (34C45) Bifurcations connected with nontransversal intersection in dynamical systems (37G25) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11) Canard solutions to ordinary differential equations (34E17)

Related Items

Spike-adding in parabolic bursters: the role of folded-saddle canards ⋮ Canard solutions in neural mass models: consequences on critical regimes ⋮ A survey on the blow-up method for fast-slow systems ⋮ Canards of Folded Saddle-Node Type I ⋮ Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system ⋮ Inflection, canards and folded singularities in excitable systems: application to a 3D FitzHugh-Nagumo model ⋮ Spike-Adding in a Canonical Three-Time-Scale Model: Superslow Explosion and Folded-Saddle Canards ⋮ On the Pitchfork Bifurcation of the Folded Node and Other Unbounded Time-Reversible Connection Problems in $\mathbb R^3$ ⋮ Canards, Folded Nodes, and Mixed-Mode Oscillations in Piecewise-Linear Slow-Fast Systems

Uses Software

• AUTO
• AUTO2000
• DLMF

Cites Work

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