Intrinsic determination of the criticality of a slow-fast Hopf bifurcation

DOI10.1007/s10884-020-09903-xzbMath1491.34069arXiv2005.10742OpenAlexW3093760323WikidataQ115383362 ScholiaQ115383362MaRDI QIDQ2665541

Peter De Maesschalck, Jeroen Wynen, Thai Son Doan

Publication date: 19 November 2021

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.10742

zbMATH Keywords

criticalityskewnessintrinsic representationsingular bifurcationsslow-fast Hopf bifurcation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Bifurcations of singular points in dynamical systems (37G10) Singular perturbations for ordinary differential equations (34E15)

Related Items (2)

Discrete geometric singular perturbation theory ⋮ Fractal codimension of nilpotent contact points in two-dimensional slow-fast systems

Cites Work

• Neural excitability and singular bifurcations
• Slow-fast Bogdanov-Takens bifurcations
• Birth of canard cycles
• Modelling, singular perturbation and bifurcation analyses of bitrophic food chains
• Stability of singular Hopf bifurcations
• Multi-timescale systems and fast-slow analysis
• Canard cycles and center manifolds
• Canard Cycles
• Two-stroke relaxation oscillators
• Geometric Singular Perturbation Theory Beyond the Standard Form
• Relaxation oscillation and canard explosion

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