On the Pitchfork Bifurcation of the Folded Node and Other Unbounded Time-Reversible Connection Problems in $\mathbb R^3$

DOI10.1137/20M1326180zbMath1470.37074arXiv2003.06817OpenAlexW3084905611MaRDI QIDQ4983499

K. Uldall Kristiansen

Publication date: 20 April 2021

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

Full work available at URL: https://arxiv.org/abs/2003.06817

zbMATH Keywords

bifurcationsblowupglobal bifurcationsFalkner-Skan equationgeometric singular perturbation theorycanardsfolded nodesecondary canardsNosé equationstwofold

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Periodic orbits of vector fields and flows (37C27) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Bifurcations connected with nontransversal intersection in dynamical systems (37G25) Canard solutions to ordinary differential equations (34E17)

Related Items

Mixed-Mode Oscillations in Coupled FitzHugh–Nagumo Oscillators: Blow-Up Analysis of Cusped Singularities ⋮ A Stiction Oscillator under Slowly Varying Forcing: Uncovering Small Scale Phenomena using Blowup

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Falkner-Skan equation. II: Dynamics and the bifurcations of \(P\)- and \(Q\)-orbits
• Local analysis near a folded saddle-node singularity
• Singularities and groups in bifurcation theory. Volume I
• Applications of centre manifold theory
• Geometric singular perturbation theory for ordinary differential equations
• Bifurcation of degenerate homoclinics
• Bifurcation of degenerate homoclinic orbits in reversible and conservative systems
• Relaxation oscillations in \({\mathbb R}^3\)
• The Falkner-Skan equation. I: The creation of strange invariant sets
• Resolution of the piecewise smooth visible-invisible two-fold singularity in \(\mathbb {R}^3\) using regularization and blowup
• Mixed-Mode Oscillations with Multiple Time Scales
• Folded Saddles and Faux Canards
• Some third-order ordinary differential equations
• The Two-Fold Singularity of Discontinuous Vector Fields
• Large amplitude oscillations for a class of symmetric polynomial differential systems in R³
• Existence and Bifurcation of Canards in $\mathbbR^3$ in the Case of a Folded Node
• Extending Melnikov theory to invariant manifolds on non-compact domains
• On the Use of Blowup to Study Regularizations of Singularities of Piecewise Smooth Dynamical Systems in $\mathbb{R}^3$
• Canards in \(\mathbb{R}^3\)