Canard cycles of finite codimension with two breaking parameters

DOI10.1007/s12346-011-0061-xzbMath1261.34044OpenAlexW2100990586MaRDI QIDQ1936486

Robert Roussarie, Lylia Mamouhdi

Publication date: 5 February 2013

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-011-0061-x

zbMATH Keywords

bifurcationLiénard equationslow-fast systemcanard cycleChebychev system

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Singular perturbations for ordinary differential equations (34E15) Relaxation oscillations for ordinary differential equations (34C26) Canard solutions to ordinary differential equations (34E17)

Related Items

Canard limit cycles and global dynamics in a singularly perturbed predator-prey system with non-monotonic functional response ⋮ Fractal analysis of canard cycles with two breaking parameters and applications ⋮ Side-comparison for transition maps in multi-layer canard problems ⋮ Singular perturbations of generalized Holling type III predator-prey models with two canard points ⋮ Slow divergence integral on a Möbius band ⋮ Multiple Buckling and Codimension-Three Bifurcation Phenomena of a Nonlinear Oscillator ⋮ 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 ⋮ Canard Cycles with Three Breaking Mechanisms

Cites Work

• Unnamed Item
• Cyclicity of common slow-fast cycles
• Bifurcation of relaxation oscillations in dimension two
• The theory of Khovanskii and the problem of Dulac.
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles
• Canard cycles with two breaking parameters
• Slow divergence integral and balanced canard solutions
• Multi-layer canard cycles and translated power functions
• Time analysis and entry-exit relation near planar turning points
• Canard solutions at non-generic turning points
• Canard cycles and center manifolds
• Multiple canard cycles in generalized Liénard equations