On the approximation of the canard explosion point in singularly perturbed systems without an explicit small parameter

DOI10.1080/14689367.2017.1313390zbMath1384.37061arXiv1504.07752OpenAlexW2602786393WikidataQ61634675 ScholiaQ61634675MaRDI QIDQ4606990

Morten Brøns, K. Uldall Kristiansen

Publication date: 9 March 2018

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.07752

zbMATH Keywords

geometric singular perturbation theorycanardtemplator model

Mathematics Subject Classification ID

Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Singular perturbations for ordinary differential equations (34E15) Canard solutions to ordinary differential equations (34E17)

Related Items (5)

Asymptotic expansions for a family of non-generic canards using parametric representation ⋮ Study of a homoclinic canard explosion from a degenerate center ⋮ Asymptotic expansions for a degenerate canard explosion ⋮ Computation of Saddle-Type Slow Manifolds Using Iterative Methods ⋮ Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exponential estimates of symplectic slow manifolds
• An iterative method for the canard explosion in general planar systems
• Chasse au canard
• Geometric singular perturbation theory for ordinary differential equations
• Multiscale geometry of the Olsen model and non-classical relaxation oscillations
• Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
• Non-standard analysis and singular perturbations of ordinary differential equations
• FROM FIRST LYAPUNOV COEFFICIENTS TO MAXIMAL CANARDS
• Canard cycles and center manifolds
• Relaxation oscillations and canards in a nonlinear model of discontinuous plastic deformation in metals at very low temperatures
• Relaxation oscillation and canard explosion

This page was built for publication: On the approximation of the canard explosion point in singularly perturbed systems without an explicit small parameter