Bifurcation of relaxation oscillations in dimension two

DOI10.3934/dcds.2007.19.631zbMath1157.34037OpenAlexW2040230701MaRDI QIDQ951278

Freddy Dumortier, Robert Roussarie

Publication date: 23 October 2008

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2007.19.631

zbMATH Keywords

bifurcationLiénard equationslow-fast systemrelaxation oscillationcanard cycle

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Singular perturbations for ordinary differential equations (34E15) Relaxation oscillations for ordinary differential equations (34C26)

Related Items (10)

A survey on the blow-up method for fast-slow systems ⋮ Smooth normal linearization of vector fields near lines of singularities ⋮ Canard cycles of finite codimension with two breaking parameters ⋮ Slow divergence integral and balanced canard solutions ⋮ Cyclicity of common slow-fast cycles ⋮ Bifurcations of multiple relaxation oscillations in polynomial Liénard equations ⋮ Multi-layer canard cycles and translated power functions ⋮ Canard Explosion and Position Curves ⋮ RELAXATION OSCILLATIONS IN SINGULARLY PERTURBED GENERALIZED LIENARD SYSTEMS WITH NON-GENERIC TURNING POINTS ⋮ Planar canards with transcritical intersections

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